A Bibliography of Publications about the Arithmetic–Geometric Mean Iteration

Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA

Tel: +1 801 581 5254 FAX: +1 801 581 4148

             E-mail: beebe@math.utah.edu, beebe@acm.org,
                       beebe@computer.org (Internet)
           WWW URL: https://www.math.utah.edu/~beebe/

17 August 2024 Version 1.27

Title word cross-reference

(a, b) ← (\frac{a+3b}{4}, \frac{\sqrt{ab}+b}{2}) [BB89]. 1 [BM88]. 2 [BM88, Gau02, KM10, KM12]. 3 [LR07]. $49.95 [Ber88]. B [SL98]. D_{4} [Sol95]. e [Has13b, Has14, YY01]. E_{6} [Sol95]. E_{8} [Sol95]. λ [SMY14]. C [CT13a]. μ [SMY14]. n [Liu94, LM70, Vas72, Yam06]. p [HM89, Xu15]. Φ [Baj78]. π [AB88, AB16, Arn11a, Bai16, BBMW16, BRT18, BB86, Hur88, Kan88, Sal76, Sal97, Sal00, Sal04, Sal16, Sin16]. q [BRS13]. U_{n} [SL98]. x^{1/x} [Sch89].

-adic [KM12, HM89, KM10]. -adique [HM89]. -convex [SMY14]. -hypergeometric [BRS13]. -like [Baj78].

-operators [Yam06]. -starlike [SMY14].

11 [Dra93a]. 11th [CGM95]. 184 [Mat95a]. 1975 [Tra76]. 1994 [Bro96].

2-adic [KM13]. 2017 [BBB^{+}20].

’88 [ML88].

94b [Mat95a]. 94c [Dra93a].

AAECC [CGM95]. AAECC-11 [CGM95]. additional [KLS00]. adic [KM12, KM13, HM89, KM10]. adique [HM89]. Advanced [Ber88, Bro96]. AGM [Ber88, TBDS92, Wim88, Arn11a, BB87, BB88, BB91, Bor95, BB98, Bor03a, Bor03b, Bor03c, Bor04c, Bor04b, Bor04a, BCF04, BC04, BDS92, Bre17, Bre20, CV91, CT13b, CT13a, Dis02, Dup11, Gau02, GOST23, KS08, Lor08, Osl15, Roo03, Sin16, Sol95, SL98, Sur01, Vil14, Ask88, Cas99]. algebra [CGM95, Mat95a]. algebraic [CGM95]. Algorithm [Nis97, Bai16, DM97, Tri65]. Algorithms [BRT18, Bre06, Car71, Gau02, Nak01, Arn11a, BB86, Bre10b, CGM95, New85, New16]. alternative [QS09]. AM [Bak16, BS12, Haj20, Hir07, Hof16, Mah20, Mal12, Mes23, MNR^{+}22, Saw17, Sch89, Shi11]. AM-GM [Sch89]. AM/GM [MNR^{+}22]. AM/GM-Based [MNR^{+}22]. among [CW13, Fur14]. amplitude [Sal89]. analogues [BR07, BBG93, Gar94]. Analysis [BBB^{+}20, Bur16, BE17, Cha14, FAB12]. Analytic [Ber88, BB87, Tra76, Wim88, BB98, Tra76]. Analytical [Par65, Par68, Par79]. analyze [FAB12]. Ando [Yam06]. Appl [Mat95a]. Application [SA06, Her72, Mar88, ZJ15, ZFFS14]. Applications [dal96, Ba97, DJ94, WQC16, Wil63, Zou17]. Applied [CGM95]. approach [CO17, DJ94]. Approximation [Rey87, Jam14, Thu72, Rey87]. Approximations [CS08, BBB16, Eng06]. April [Tra76]. arbitraire [Bol99]. arbitrary [Bol99, GQ03]. arc [Alm78]. Arch [Dra93a]. argument [Dij94, Dij96a]. Arithmetic [Ake63, AFL96, AB88, Als00, Bel14, BS93a, BD93, BB83, BB84b, BB84a, BLM96, BB97, BLM97, BB00, BB04, Bur87, But36, CR16, Car70, Car71, CN87, Cox97, Cox00, Cox04, Cus81, Dia60, Eve63, FP84, Gai67, Gen18, GM03, GT20, Hor95, Kat03, KP96a, Kos98, LR07, LO96, Mar88, MT10, MNC71, Min87, Nel87, Nel89, Nel15, Neu96, O’S68, PM82, Pla20, RLC09, Sal76, Sal97, Sal00, Sal04, Sch86, Sch78, Sch82, Sch88, Sch84, Toa98, WCW11, WCW12, Xie02, Yan00, YY01, Abr79, ABK16, Aiy45, Alb12, Ald08, Ald09, Ald10, Ald11, Ald12, AMPV97, ABPV97, Alm78, AB16, Alz87, Alz88, Alz89, Alz90b, Alz90f, Alz90c, Alz90d, Alz90e, Alz90a, Alz91, Alz92a, Alz92b, Alz94, Alz95, Alz96, Alz97, Alz99, AR02, And83, Aud15, Ba97]. arithmetic [Baj78, BR07, Bel56, Ben93, Ben94, Ben95, Ben98, BK00, Bha06, BK08, Bol99, Bor87, Bor88a, Bor88b, Bor88c, Bor88d, Bor88e, Bor88f, Bor89, BBG93, BB16b, Bra01, Bul67, Bul04, Bul91, BE15, CMN71, CF78, CS08, CB11, CO17, Cha02, CE09, CS17, Cho76, Cho77, CZW11, CW11, CW12, CWQ12, CW13, CWQM13, CQWZ15, Chu90, Chu12, CL92, Cox84, Cox85, Cox16, CK13, Dij92, Dij94, Dij96a, Dij96b, DZ17, DM97, Dob01, DL99, Dra93a, Dra93b, DCP97, Dra98, Dra99, DJ94, EN01, Eve67, Eve69, Fen95, FT08, FJ76, Fin81, Fou99, FLFJ11, FAB12, FFSZ16, Fur14, Fur94, Gao15, Gar94, Gas97, Gau92, Geo02, Gep28, Gla76, GSWC12, GM17, GHT11, GT13, GQ03, GZCS16, Hao93, Hao00, Har91, Has13a, Has13b, Has14, Hay09, HZQ12, HC12, Hei81]. arithmetic [HM89, Her72, Hir16, Hol06, HM86, Hun56, Hun27, IKW16, Ito08, Jam14, Jam18, Jar08, JK99, Kan88, Kan16, KL96, KL98, KP96b, Ked94, KL07, KLL09, KLL11, KM10, KM12, KM13, Kit92, KKLP12, Kla68, Kno03, Kob58, KS07, KMS79, KL12, KS00, KLS00, Lan78, Lat99, LL11, Lek09, LQ15, Lin91, Liu94, LZ06, LGSC13, LM70, LC10, LC11, Luc95, MV10, Mat10, Mat93, Mat95a, Mat95b, MW12, Mer03, MPŠ08, Mih05, Mit66, Mit70, Mol11, Mon03, MH72, Mur97, Nak01, Nan80, Nan46, Nis88, Nis94, Nis97, NC88, NC90, Ono83, Opp65, Opp68, OT04, Peč95, PM97, PV97, Pee89, Pin15, Pla22, Qi03a, Qi03b, QS09, QC14, QCZ15, Rau42, Raz86, Rey87, Rod17, RM92, Roy03, Rua15, SA06, ST94, Sal89, Sal16, SM99, Sán90, Sán99]. arithmetic [SK77, Sch11, Sei87, Sei97, Sen87, Seo12, SZ13, She16, She17, Shi66, SA10, SvS12, SMY14, Ste96, Stu44, Tan06, Tan07, Tor56, Tun75, Uch08, Vas72, WW07, WY88, Wan99, WCJQ14, WZSC14, WQC16, Waz91, Wil63, Wu17, XHWC12, Xu15, Xue17, YMT10, Yam13, YYWQ14, YSC14, Yan14, YYC08, ZX11, ZWCL14, ZJ15, ZH15, ZJ16, Zou17, Zou19, Zul86, ZFFS14, ZC15, dal96, BT11, BM88, Edd85, MP88, Nel95, OC14]. Arithmetic-Geometric [Sch78, Sch82, Sch88, Zou19, Edd85]. Arithmetic-Logarithmic-Geometric [Nel95]. arithmetic-mean [JK99, Ked94, Wan99]. arithmetic-mean-geometric-mean [Cho77]. arithmetico [Sur00, Bol99, BM88, HM89, Rey87]. arithmético-géométrique [Bol99]. arithmetisch [Gep28, Hei81, Sch11]. arithmetische [Alz88, Alz90f]. arithmetischen [Alz87, Sei87]. aritmet [Gau17]. aritmético [Gau92]. aritmeticorum [Gau92]. Aritmetisk [Alm78]. aspects [Tan06]. associated [DCP97, Eve67, Eve69, Nak01, Tan07]. Asymptotes [BB93]. Asymptotic [BE15, Bur16, BE17]. August [Bro96]. Australia [BBB^{+}20]. Automated [Zha96]. automatic [AK93]. average [FLFJ11]. averages [Alz88]. averaging [FLFJ11]. Axially [Lek09].

B [Ask88, Ber88, MNC71, TBDS92, Wim88]. Båglängd [Alm78]. backlogging [CO17, OC13]. backorders [CB10a]. Barzilai [IP17]. Based [MNR^{+}22, CS08, DM97, Kno03, Pla22, RM92, Roy03, Waz91]. bcc [MH71]. be [Mal98]. Behold [Edd85, MP88]. Bernoulli [Mal12]. Best [Kno03]. Between [Gen18, WCW11, WCW12, Abr79, Ald08, Ald09, Ald10, Ald11, Ald12, Alz87, Alz90d, Aud15, Cha02, CE09, CW11, CW12, GSWC12, HC12, Hol06, KLS00, Lan78, Lat99, LQ15, LM70, Pin15, Sei87, Shi66, Tun75, WZSC14, ZJ16]. bi [SMY14]. bi- [SMY14]. biased [Sen87]. billion [BBB16]. binomial [Roo03]. Birth [AAS16]. bivariate [Roy03]. Book [Ber88, Cas99, MNC71, TBDS92, Wim88, BBB97, BBB00, BBB04]. bootstrapping [Shi11]. Borchardt [Bor88f, Tri65]. Borwein [Ask88, Ber88, Wim88, Ask88, Bre17, Bre20, IP17]. Borweins [Bai16]. bound [ABK16, Alz90d, LQ15, ZFFS14]. bounding [QS09]. Bounds [Hor95, PM82, WCJQ14, Ald12, CZW11, CWQ12, CWQM13, CQWZ15, DZ17, GZCS16, Kno03, LGSC13, LC11, Pin15, QC14, QCZ15, ST94, SZ13, Tun75, WQC16, XHWC12, YYWQ14, YSC14, Yan14]. Boyer [KP96a, KP96b]. Brent [New85, New16]. Brothers [Bre20]. busque [Gau92].

C [MNC71, TBDS92]. Calabi [MT10].

Calcul [Bol99]. Calculation

[BB84c, Kin21, Kin24, Kin07, MH71, Kan88, Kan16, MH72, Sal89]. calculations [Tri66]. Calculus [Hof16, Min87, Sch78]. Callaghan [BBB^{+}20]. called [Mal98]. Canadian [Ber88]. Canonical [Car11]. Carlson [TBDS92]. Carnegie [Tra76]. Carnegie-Mellon [Tra76]. case [Bor04c, Bor04b, BCF04, BC04]. categories [YMT10]. Cauchy [Aud15, ZJ16]. Celebration [BBB^{+}20]. Certain [Sán96, Leh71]. chain [Cha14, Chu12]. Characteristic [Gau02]. Characterization [Roy03]. Characterizations [RM92, Har91]. charge [Lek09]. chosen [FLFJ11]. Circles [Kin21]. class [Eng06]. classical [FLFJ11]. Classroom [Ake63, Dia60, Gai67]. closed [JK99]. cm [Ber88]. Coaxial [Kin21]. codes [CGM95]. coefficient [SMY14]. Combination [Gau02, CZW11, HC12, LC11, XHWC12, YYWQ14]. combinations [CWQ12]. combinatorial [Hao00]. Comment [Abr79]. commutative [Hay09]. Comparison [Ald11, Gau02, HK99, FAB12]. complete [MH72, OC13, WQC16]. Complex [LO96, AR02, Bor04b, BC04, CT13b, CT13a, Fou99, MH72, Nis97, Tor56]. complex-parameter [BC04]. Complexity [BB84c, BB87, BB98, Bre76b, Bre10a, Eng06, Tra76, Ber88, Wim88]. composition [MV10]. compositions [Hol06]. Compound [BB93, BE17]. compounding [Leh70, Leh71]. Computation [BRT18, BB84b, BB97, BB00, BB04, Bre06, BE17, CR16, Sal76, Sal97, Sal00, Sal04, Sal16, AAS16, Bai16, BBMW16, BB16a, BBP16, Bol99, BB16b, Eng06, IP17]. Computational [Arn11b, Ber88, BB87, Wim88, BB98, Tra76]. Computations [Krä93, Hur88, Kar93]. compute [BBB16, CB10b]. Computer [AFL96, Tra76, Pee89]. computers [Tri66]. Computing [BRT18, Dis02, AK93, AFL96, Arn11a, BI11]. concave [Lat99]. Concentration [Ald10]. concerning [Kla68, Mit66]. condition [BS12]. conditions [WZSC14]. conjectures [CL92]. connected [KL96, KL98, OT04, SMY14]. connecting [Opp65, Opp68, Vas72]. consistent [FLFJ11]. Constant [YY01]. constants [BBP16]. Construction [SL98, SA06]. containing [Ba97]. contingency [YMT10]. Continued [Bor03a, Bor03b, Bor03c, Bor04c, Bor04b, Bor04a]. Continuous [Mol11, FAB12]. contra [YYWQ14]. contra-harmonic [YYWQ14]. contraharmonic [CQWZ15]. Contribution [But36]. Convergence [Lor08, MH72]. convergent [Bai16]. converging [BB86]. converse [Alz90b, KL07, KLL09]. convex [AB07, CZW11, Hir16, KL12, SMY14, XHWC12]. Convexity [NC90, Xu15]. Corollaries [Pla20]. correcting [CGM95]. corresponding [KS08]. Corrigendum [Eve69]. Counterpart [BB88, BB91]. Counterparts [Dra99]. Counting [Gau02]. courbes [BM88]. course [Tka03]. covariates [SA06]. criteria [KL96, KL98, OT04]. Cubic [BB88, Gar94, BB91, Bor95]. Curves [Gau02, GOST23, BM88, CT13b, CT13a, DL99, KM10, MT10].

data [FAB12]. decimal

[Bai16, Kan88, Kan16]. Decimals [BRT18]. Deductive [Bro96, Bro96]. definite [And83, KL07, KLL09, ST94, Yam13]. del [Tri65]. delay [OC13]. Department [Tra76]. derive [CB10a]. derived [JK99]. design [Bro96]. deteriorating [Cha14]. determinantal [BT11]. determining [CO17]. developments [FFSZ16]. Diary [AB88, AB16]. difference [Ald12, Alz90d, GQ03, LM70, Pin15, Qi03a, Qi03b, SZ13, Tun75]. differences [Ald11, FAB12]. Differential [CK13, LL11]. digits [AAS16, Bai16, BBMW16, BBB16, Kan88, Kan16]. Dimensional [Kat03, Bor88f]. Direct [Kin24, Kin07, SM99]. disc [Fou99]. discovered [Bor95]. discrete [Alz95, Gao15]. dispute [CB11]. distance [CB11]. Distant [BRT18]. Distribution [Lin91, Gla76, HM86, Nan80, Roy03]. distributions [Lek09, Nan80]. divergence [Lor08, Tan06]. do [Sen87]. Double [WCW11, WCW12, GSWC12, Lin91, QS09]. Dynamics [Bor04c, Bor04b, Bor04a, Bul91, Par65, Par68, Par79].

easy [CB10a]. echelon [Cha14]. economic [CB10b]. Edgeworth [HM86]. Eigenvalue [AB07]. electronic [Tri66]. élémentaires [Bol99]. Elementary [BB84b, BB97, BB00, BB04, Bre75, Bre76a, Bre06, Hof16, Min87, Bol99, BB16b, Bre76b, Bre10a, Bre10b, Bre16, Mit70, Yam13]. ellipse [Alm78, Sur00, WCJQ14]. Ellipsens [Alm78]. Ellipses [AB88, AB16]. Elliptic [Gau02, GOST23, Kin24, Kin07, Tka03, Arn11a, CT13b, CT13a, KM10, Mon03, MH72, Wac00, WQC16]. empiric [FAB12]. Entropy [GT20, ABK16]. EOQ [CB10a]. EPQ [CB10a]. equality [BS12]. equation [Zul86]. equations [BBB16, MV10, Wil63]. equivalence [Lat99, MV10]. Equivalent [Mal12, YYC08]. Errata [Dra93a]. Erratum [Mat95a]. error [CGM95, Mon03]. error-correcting [CGM95]. Eshelby [FLFJ11]. estimates [SMY14]. Euclidean [Dob01, SA10]. Evaluating [Wac00]. Evaluation [Bre75, Bre76a, Bre76b, Bre10a, Bre16, Dup11]. every [Fur94]. Exact [BRT18, Pin15, Bol99, Nan80]. Excursion [Bor87, Bor88a, Bor88b, Bor88c, Bor88d, Bor88e]. expansion [BE15, HM86, Roo03]. expansions [BE17]. experiment [Pee89]. Explicit [LR07]. exponential [Lin91]. extended [KS08]. extending [Wu05]. extension [Tor56, Yam06]. Extensions [Fou99, Had12]. external [Seo12]. Extremum [MP88].

failure [RM92, Roy03]. Fast [BB84b, BB97, BB00, BB04, Bre75, Bre76a, Bre06, Bre16, Dup11, BB16b, DM97, New85, New16]. fcc [MH71]. Fibonacci [Sch84]. field [Tor56]. fields [KM12, KM13]. find [Sur00]. finding [Bre76b, Bre10a]. finite [Her72]. first [CQWZ15]. floating [Eng06]. Florida [ML88]. fonctions [Bol99]. Form [Sch88, KS07]. Formal [BRT18]. Forms [BD93, KS08, YYC08]. Formula [LR07, Seo12]. Formulae [Kin21]. formulas [KS07, OC14]. four [Bor88f]. four-dimensional [Bor88f]. Fraction [Bor03a, Bor03b, Bor03c, BCF04, BC04, Lor08]. Fractions [Bor04c, Bor04b, Bor04a]. France [CGM95]. French [Bol99, BM88, HM89, Rey87]. function [Bre76b, Bre10a, Mit70, MH71, Nis15, Pla22, Sal89]. function-based [Pla22]. functional [MV10, Zul86]. functionals [LL11]. Functions [BB84b, BB97, BB00, BB04, Bre75, Bre76a, Bre06, Kin24, Kin07, LO96, AB07, BRS13, Bol99, BB16b, Bre10b, Bre16, Dup11, Gar94, Gas97, Hir16, JK99, KL12, Naj13, SMY14, Tka03, Tri66, Wac00].

Galois [Car11]. gamma [Gla76, Nan80]. Gaus [Sch11]. Gauss [AB88, AB16, Bor87, Bor88a, Bor88b, Bor88c, Bor88d, Bor88e, CWQM13, Cox84, Cox85, Cox97, Cox00, Cox04, Cox16, Har91, KS08, MV10, Nis88, Nis94, Ono83, Sán99, Sch11, Sur00, Tan07]. Gaussian [WQC16]. General [Sch88]. generalibus [Gau17]. generalis [Gau92]. generalization [EN01, FJ76, Hei81, Her72, Hun56, Ono83, Tri65]. Generalizations [Kat03, NC88, NC90]. Generalized [BB83, BB84a, Eve63, Pas71, Sch84, Tan06, Xie02, CW13, DZ17, LC10, LC11, Mat10, SvS12, WZSC14, ZX11]. Generalizing [Pee89]. generalizzazione [Tri65]. generated [Szy91]. generation [BB16a]. genre [BM88]. Genus [LR07, BM88, DL99, Jar08]. Geometic [MP88]. Geometric [Ake63, AB88, Als00, BT11, BS93a, BD93, BB83, BB84b, BB84a, BLM96, BB97, BLM97, BB00, BB04, Bur87, But36, CR16, Car70, Car71, Cox97, Cox00, Cox04, Cus81, Dia60, Eve63, Gai67, Gen18, GM03, GT20, Hor95, Kat03, KP96a, Kos98, KK09, LR07, LO96, MNC71, Min87, Nel87, Nel89, Nel15, Neu96, O’S68, OC14, PM82, Sal76, Sal97, Sal00, Sal04, Sch86, Sch78, Sch82, Sch88, Sch84, Toa98, WCW11, WCW12, Xie02, YY01, Abr79, ABK16, Aiy45, Alb12, Ald08, Ald09, Ald10, Ald11, Ald12, AMPV97, ABPV97, Alm78, AB16, Alz87, Alz88, Alz89, Alz90b, Alz90f, Alz90c, Alz90d, Alz90e, Alz90a, Alz91, Alz92a, Alz92b, Alz94, Alz95, Alz96, Alz97, Alz99, AR02, And83, Aud15, Ba97, Baj78, BR07, Bel14, Bel56, Ben93, Ben94]. geometric [Ben95, Ben98, BK00, Bha06, BK08, BI11, Bol99, Bor87, Bor88a, Bor88b, Bor88c, Bor88d, Bor88e, Bor88f, Bor89, BBG93, BB16b, Bra01, Bul67, Bul04, Bul91, BE15, CMN71, CF78, CS08, CB11, CO17, Cha02, CE09, CS17, Cho76, Cho77, CZW11, CW11, CW12, CWQ12, CW13, CWQM13, CQWZ15, Chu90, Chu12, CN87, CL92, Cox84, Cox85, Cox16, CK13, Dij92, Dij94, Dij96a, Dij96b, DZ17, DM97, Dob01, DL99, Dra93a, Dra93b, DCP97, Dra98, Dra99, DJ94, EN01, Eve67, Eve69, Fen95, FT08, FJ76, Fin81, Fou99, FLFJ11, FAB12, FFSZ16, Fur14, Fur94, Gao15, Gar94, Gas97, Gau92, Geo02, Gep28, Gla76, GSWC12, GM17, GHT11, GT13, GQ03, GZCS16, Hao93, Hao00, Har91, Has13a, Has13b, Has14, Hay09, HZQ12, HC12, Hei81, HM89, Her72, Hir16, Hol06]. geometric [HM86, Hun56, Hun27, IP17, IKW16, Ito08, Jam14, Jam18, Jar08, JK99, KL96, KL98, KP96b, Ked94, KL07, KLL09, KLL11, KM10, KM12, KM13, Kit92, KKLP12, Kla68, Kno03, Kob58, KS07, KMS79, KL12, KS00, KLS00, Lan78, Lat99, LL11, Lek09, LQ15, Lin91, Liu94, LZ06, LGSC13, LM70, LC10, LC11, Luc95, MV10, Mar88, Mat10, Mat93, Mat95a, Mat95b, MT10, MW12, Mer03, MPŠ08, Mih05, Mit66, Mit70, Mol11, Mon03, MH72, Mur97, Nak01, Nan80, Nan46, Nis88, Nis94, Nis97, NC88, NC90, Ono83, Opp65, Opp68, OT04, Peč95, PM97, PV97, Pee89, Pin15, Pla22, Qi03a, Qi03b, QS09, QC14, QCZ15, RLC09, Rau42, Raz86, Rey87, Rod17, RM92, Roy03, Rua15, SA06, ST94, Sal89, Sal16, SM99, Sán90, Sán99, SK77, Sch11]. geometric [Sei87, Sei97, Sen87, Seo12, SZ13, She16, She17, Shi66, SA10, SvS12, SMY14, Ste96, Stu44, Sur00, Tan06, Tan07, Tor56, Tun75, Uch08, Vas72, WW07, WY88, Wan99, WCJQ14, WZSC14, WQC16, Waz91, Wil63, Wu17, XHWC12, Xu15, Xue17, YMT10, Yam06, Yam13, Yan00, YYWQ14, YSC14, Yan14, YYC08, ZX11, ZWCL14, ZJ15, ZH15, ZJ16, Zou17, Zou19, Zul86, ZFFS14, ZC15, dal96, Edd85, Nel95, BM88]. geometric-harmonic [Mat93, Mat95a, ST94, Ste96]. geometric-harmonic-mean [And83]. geometric-mean [GM17, JK99, Ked94, Kit92, Wan99]. geométrica [Gau92]. Geometrical [Shi66]. geometricorum [Gau17, Gau92]. géométrique [Bol99, BM88, HM89]. géométriques [Rey87]. geometrische [Alz88, Alz90f]. geometrischen [Alz87, Gep28, Hei81, Sch11, Sei87]. geometriska [Alm78]. geometry [Dob01]. German [Alz87, Alz88, Alz90f, Gep28, Hei81, Sch11, Sei87]. Germany [AFL96, Bro96]. gewichtete [Alz90f]. Gini [CW12]. GM [Bak16, BS12, Haj20, Hir07, Hof16, Mah20, Mal12, Mes23, Saw17, Sch89, Shi11]. GM-Based [MNR^{+}22]. good [Thu72]. Gradient [Mah20]. graphs [Ber88]. Green [MH71]. growth [AAS16]. Guarantees [BRT18]. Guesstimation [KK09].

Hadamard [Hor95, Mat93, Mat95a].

hapless [Pee89]. Harmonic

[FP84, Nel87, Nel89, Pla20, Sch84, YMT10, AMPV97, Alz90c, Alz90a, Alz95, And83, Bel14, CB11, CS17, CW11, Dra99, Fur14, HC12, Hun27, KLL11, Kla68, KL12, LC11, Mat93, Mat95a, MW12, Mer03, Nak01, Pla22, QCZ15, RLC09, RM92, Roy03, ST94, Sen87, Shi66, SA10, Ste96, WW07, WCJQ14, WZSC14, YYWQ14]. harmonic-mean [AMPV97]. Heinz [GHT11, HZQ12, KKLP12, ZWCL14]. held [AFL96, Bro96, Tra76]. Hellinger [DJ94]. Heron [ZWCL14]. Heuristic [KK09]. heuristics [Dij94, Dij96a]. High [Bre06]. High-Precision [Bre06]. Higher [Jar08, DL99, KL07]. Hilbert [KKLP12, ZC15]. history [BB16a]. Hölder [Kob58, Mal98, Zou19]. Holomorphic [Nis94, Nis88]. Hyperelliptic [SvS12, MT10]. Hypergeometric [BBG93, KM12, KM13, BRS13, BR07, Gar94]. identities [Gar94]. Identity [BB88, Sin16, BT11, BB91]. Identric [Neu96, Sei97]. II [BC04, KL96, Nan46, Nis94, Opp68, Sán96]. III [Aiy45]. imperfect [CO17, OC13]. Improved [KKLP12, ZJ15, ZC15, GT13, HZQ12]. improvement [Ald09, Dra98]. inaccessible [BBMW16]. included [Dij94, Dij96a]. independent [Hun27]. Induction [Kin21, Zha96]. inductive [BS12, Mat95b, Mes23, SM99]. Ineqality [Nel87]. Inequalities [Alz90c, Alz92a, BB93, CS17, CW12, CW13, GQ03, Kla68, Kos98, MPŠ08, Nan46, Neu96, Qi03a, Qi03b, Sán96, VV94, WY88, Alb12, AMPV97, Alz95, Alz99, And83, Aud15, AB07, Ba97, BRS13, BR07, BK00, Bul67, BE15, CW11, FKY09, Fur14, GHT11, GT13, HZQ12, HC12, Ito08, Kit94, Kit99, KKLP12, Liu94, LC10, MW12, Mer03, Mih05, Mit70, Naj13, Opp65, Opp68, PM97, Pla22, Sei97, Shi66, Ste96, Tao06, Vas72, WZSC14, Wu05, Wu17, Xue17, Yan00, ZWCL14, ZJ16, Zou19, ZC15, Alz88]. Inequality [Ake63, Als00, BS93a, BD93, BDS92, Bur87, Car70, CV91, Cus81, Dia60, Eve63, Gai67, Gen18, GM03, GT20, Hof16, Hor95, Kat03, Mah20, Mal12, MNC71, Min87, Nel89, Nel15, O’S68, Saw17, Sch86, Sch78, Sch82, Sch88, Sch89, Shi11, WCW11, WCW12, YY01, Abr79, ABK16, Ald08, Ald09, ABPV97, Alz87, Alz89, Alz90b, Alz90e, Alz91, Alz92b, Alz96, Alz97, AR02, Bak16, Bel56, Ben93, Ben94, Ben95, Ben98, Bha06, BK08, Bra01, Bul04, CF78, CO17, Cha02, CE09, Cho76, Cho77, Chu90, Dob01, Dra93a, Dra93b, Dra98, Dra99, Eve67, Eve69, Fen95, FT08, FJ76, Fin81, Fou99, FFSZ16, Fur94, Gao15, Geo02, GSWC12, Haj20, Hao93, Hao00, Has13a, Hay09, Her72, Hir07, Hir16, Hol06, Hun56, IKW16, JK99, Ked94, KL07, KLL09, Kit92]. inequality [Kno03, Kob58, KMS79, KS00, Lan78, LZ06, Luc95, Mat10, Mat93, Mat95a, Mat95b, Mes23, Mit66, Mur97, Peč95, PV97, QS09, Rod17, Roo03, Rua15, SA06, SM99, Sán90, SK77, Seo12, She17, Uch08, Wan99, Wil63, Yam06, Yam13, YYC08, ZJ15, ZH15, Zou17, dal96, Edd85, Mal98, MP88, Nel95, TBDS92]. Initial [SMY14]. Institute [Bro96]. integers [Has14, KMS79]. integrable [Nak01]. integral [WQC16]. Integrals [Kin24, Kin07, Arn11a, DJ94, MH72, SvS12]. Interaction [KP96a, KP96b]. International [AFL96, CGM95]. Interpolating [Aud15, Bha06]. interpolation [DJ94, ZJ16]. interpretation [WW07]. interpretations [Shi66]. Introduction [Tka03]. invariance [ZX11]. Invariant [Hor95, Fur94, Zou19]. inventory [CB10a, Cha14]. inverses [Wac00]. Involving [Car71, Alz95, Bul67, CK13, MV10, Mat93, Mat95a, MPŠ08, Mit70, SZ13, ZWCL14]. Irreducibility [Had12]. isogenies [DL99]. Isogeny [KS07]. Italian [Tri65]. items [Cha14]. Iteration [BB89, BBG93, Gar94]. Iterations [BB93, SL98, Dup11]. iterative [Bur16, Tri65]. iterativo [Tri65].

Jacobi [BB88, BB91]. Jacobian [Sal89]. Jellyfish [GOST23]. Jensen [ZFFS14]. Jonathan [Wim88, Ask88, BBB^{+}20, Ber88, Bre17]. Jugendarbeiten [Sch11]. July [Bro96, CGM95]. Justification [KK09].

Kantorovich [Yam06]. known [Har91]. Kröner [FLFJ11]. Kwong [Naj13].

Ladies [AB88, AB16]. Landen

[AB88, AB16]. Latin [Gau17]. lattice [MH71]. Lattices [SL98, MH71]. law [Wan99]. Lectures [Tri66]. Legacy [BBB^{+}20]. Legendre [Bor87, Bor88a, Bor88b, Bor88c, Bor88d, Bor88e, Sin16]. Lehmer [CWQ12, WCW11, WCW12]. lemniscate [Nis15]. length [Alm78, Sen87]. length-biased [Sen87]. Li [Yam06]. Life [BBB^{+}20]. like [Baj78]. limit [Eve67, Eve69]. limits [Nis97]. line [IP17]. linear [NC88, Mat95a]. locate [Chu12]. Log [BB84c, AB07, HM86, Lat99]. log-concave [Lat99]. log-convex [AB07]. Logarithm [CR16, Sur01]. Logarithmic [BB93, BDS92, Bur87, CV91, Pla20, TBDS92, CW11, CW13, CWQM13, DZ17, Liu94, LC10, LC11, Mat10, Nel95]. logarithms [CT13b, CT13a]. logical [Szy91]. Lorentz [Mar88]. lot [CO17, OC13]. lower [Alz90d, Pin15, ST94, SZ13, Tun75].

M [Ask88, BBB^{+}20, Ber88, TBDS92, Wim88]. Mapping [Rau42]. mappings [DCP97]. maps [Mol11]. Marktoberdorf [Bro96]. Mathematical [Ber88, Cus81, O’S68, Zha96]. Mathias [Yam06]. matrices [ABPV97, And83, CN87, FKY09, GHT11, HZQ12, IKW16, Kit92, Mol11, ST94, She17, SA10, Tao06, Wu17, Yam13]. Matrix [BD93, CR16, FT08, LO96, AMPV97, Aud15, BK00, BK08, BI11, FFSZ16, Fur94, GT13, IP17, KLL11, PM97, ZJ16]. Matters [Arn11b]. Mean [Ake63, AB88, Als00, BS93a, BD93, BB83, BB84b, BB84a, BB89, BB93, BB97, BB00, BB04, BDS92, Bur87, But36, CR16, CV91, Cox97, Cox00, Cox04, Cus81, Dia60, Edd85, FP84, Gai67, GM03, GT20, Hor95, Kat03, KP96a, Kos98, KK09, LR07, LO96, Min87, MP88, Nel87, Nel89, Nel15, O’S68, Pas71, PM82, Sal76, Sal97, Sal00, Sal04, Sch86, Sch78, Sch82, Sch88, Toa98, YY01, Abr79, ABK16, Alb12, AMPV97, ABPV97, Alm78, AB16, Alz87, Alz89, Alz90b, Alz90f, Alz90e, Alz90a, Alz91, Alz92b, Alz96, Alz97, AR02, And83, Aud15, Ba97, BR07, Bel56, Ben93, Ben94, Ben95, Ben98, BK00, Bha06, BK08, Bol99, Bor87, Bor88a, Bor88b, Bor88c, Bor88d, Bor88e, Bor88f, Bor89, BBG93, BB16b, BM88, Bra01, Bul04, Bul91]. mean [BE15, CF78, CS08, CO17, Cha02, CE09, Cho76, Cho77, CZW11, CWQ12, CWQM13, Chu12, Cox84, Cox85, Cox16, Dij92, Dij94, Dij96a, DZ17, Dob01, DL99, Dra93a, Dra93b, Dra99, DJ94, EN01, Eve67, Eve69, Fen95, FT08, FLFJ11, FAB12, FFSZ16, Fur14, Fur94, Gao15, Gar94, Gau92, Gep28, Gla76, GM17, GT13, Har91, Has13a, Hay09, HZQ12, HC12, Hei81, HM89, Her72, Hir16, HM86, Hun27, IP17, IKW16, Jam14, JK99, KP96b, Ked94, KLL11, KM10, KM12, KM13, Kit92, Kno03, KS07, KL12, KS00, KLS00, Lan78, Lek09, LQ15, Lin91, Liu94, LZ06, LGSC13, LM70, LC11, Luc95, MV10, Mat93, Mat95a, Mat95b, Mer03, Mol11, Mon03, MH72, Mur97, Nan80, Nis88, Nis94, Nis97, NC88, NC90, Peč95, PM97, PV97, Pee89, Pla22, QS09]. mean [QCZ15, RLC09, Rau42, Raz86, Rua15, SA06, Sal89, Sal16, SM99, Sán99, SK77, Sch11, Sei87, Seo12, SZ13, She16, She17, SvS12, Ste96, Sur00, Tan06, Tor56, Tun75, Uch08, WW07, Wan99, WZSC14, WQC16, Wu17, XHWC12, XGW13, Xu15, Xue17, Yam06, Yam13, Yan00, YSC14, Yan14, YYC08, ZX11, ZJ15, ZH15, ZJ16, Zou17, Zou19, BT11, Nel95, OC14, TBDS92]. Mean-Geometric [GT20, Alz91, Alz92b, CF78, Cho76, Dra93a, Dra93b]. Mean-Harmonic [Nel89]. meaning [FLFJ11]. Means [BLM96, BLM97, Car70, Car71, Eve63, Gen18, HK99, Neu96, Pla20, Sán96, Sch84, VV94, WCW11, WCW12, Aiy45, Ald08, Ald09, Ald10, Ald11, Ald12, Alz90c, Alz90d, Alz92a, Alz94, Alz95, Alz99, Baj78, Bel14, BI11, Bul67, Bur16, BE17, CMN71, CB11, CS17, CZW11, CW11, CW12, CWQ12, CW13, CQWZ15, Chu90, CN87, CL92, CK13, Dij96b, DZ17, DM97, DCP97, Dra98, FJ76, Fin81, Fou99, FAB12, Gas97, Geo02, GSWC12, GHT11, GQ03, GZCS16, Hao93, Hao00, Has13b, Has14, HC12, Hol06, Hun56, Ito08, Jam18, Jar08, KL96, KL98, KL07, KLL09, KLL11, KKLP12, Kla68, Kob58, KMS79, KL12, Lat99, LL11, Leh70, Leh71, LGSC13, LC10, LC11, Mar88, Mat10, MT10, MW12, MPŠ08, Mih05, Mit66, Mit70, Nak01, Nan46, Ono83, Opp65, Opp68, OT04, Pin15]. means [Qi03a, Qi03b, QC14, QCZ15, Rey87, Rod17, RM92, Roy03, ST94, Sán90, Sei97, Sen87, Shi66, SA10, SMY14, Stu44, Tan07, Vas72, WY88, WCJQ14, WZSC14, Waz91, Wil63, XHWC12, YMT10, YYWQ14, Yan14, ZX11, ZWCL14, Zul86, ZFFS14, ZC15, dal96, MNC71]. measure [Tan06, WW07]. measures [Lat99, YMT10]. Medelvärdet [Alm78]. media [Gau92]. mediorum [Gau17, Gau92]. Mellon [Tra76]. meta [FAB12]. meta-analysis [FAB12]. method [CB10a, CB10b, Chu12, FLFJ11, IP17, Raz86]. methods [Bre76b, Bre10a, Waz91]. minimum [CB11]. Mittel [Sei87, Alz87, Sch11]. Mittels [Gep28, Hei81]. Mittelwerte [Alz88, Alz90f]. Mixed [Car70, CMN71, Ito08, MNC71, Ba97, Gao15, Ked94, Mat95b]. model [FLFJ11]. models [CB10a, Cha14]. Modified [Waz91]. modular [BBB16, Dup11, Gar94, KS07, KS08]. modulus [MH72]. Mono [Ber88]. Mono- [Ber88]. monotonicity [GQ03, Qi03a, Qi03b]. Moore [KP96a, KP96b]. Moyenne [BM88, HM89, Bol99]. moyennes [Rey87]. MR1209383 [Mat95a]. MR1220829 [Dra93a]. Muirhead [WZSC14]. Multiple [Bre75, Bre76a, Bre76b, Bre10a, Kar93, Krä93, LO96, Bre16, Kan88, Kan16]. Multiple-Precision [Bre76a, Krä93, LO96, Bre75, Bre76b, Bre10a, Kar93, Bre16, Kan88, Kan16]. Multivariable [Hof16]. music [Bel14]. Mutual [Kin21].

NATO [Bro96]. Necessary [WZSC14].

Negative [Min87]. Nested [Osl15]. Neuman [GZCS16, QC14, YYWQ14]. Newton [Dup11]. next [BB16a]. Nieuw [Dra93a]. no [Dra93a]. nominal [YMT10]. Non [Hay09, Dob01]. Non-commutative [Hay09]. non-Euclidean [Dob01]. noncommuting [NC88]. noncontinuous [EN01]. nonlinear [dal96]. nonmonotone [IP17]. Norm [Hor95, Aud15, Fur94, Kit99, ZJ16]. normalized [Nan80]. Norms [Hor95, GT13, SA10, Zou19]. Note [Alz94, Chu90, GM03, Tor56, Wu17, Alz91, BI11, Fur94, Jam18, Kit92, MW12, SA10, Ste96, ZJ16]. Notes [Ake63, BK00, Bur87, Cus81, Dia60, Gai67, Min87, O’S68, Rua15]. novel [Tan07]. November [ML88]. Number [Ber88, BB87, Wim88, BB98, Has13b, Has14]. Numbers [Als00, Min87, AR02, Has13b, Opp65, Opp68, Sei87, Vas72]. Numerical [Kin21, Kin24, Kin07, She16, She17, Waz91]. numerics [AFL96]. numerorum [Gau17, Gau92].

observations [CB10b, CL92]. once

[Dij96b]. one

[BBB16, HC12, Mat10, Tri65, XHWC12]. one-parameter [HC12, XHWC12]. ones [Her72]. operation [Tan07]. Operator [Fur14, ZWCL14, Bak16, Bha06, Kit94, LZ06, MPŠ08, ZFFS14]. operator-trace [LZ06]. Operators [HK99, Kos98, Alb12, Hir16, KL07, KLL09, Kit99, KKLP12, NC88, RLC09, She16, Szy91, Xue17, Yam06, Yan00, ZC15]. Optimal [CZW11, CW11, CWQ12, CQWZ15, DZ17, HC12, LC10, LC11, OC13, QC14, WQC16, XHWC12, CO17, Chu12, Mat10, YYWQ14]. Optimization [MNR^{+}22]. order [CB10b, KL07]. origene [Gau17, Gau92]. Orlando [ML88]. Ostrowski [Had12]. other [Har91]. outcomes [FAB12]. overweighted [Alz90f].

packing [XGW13]. parallel [SA06]. parameter [BCF04, BC04, CWQM13, HC12, XHWC12]. parameterized [KLL11, KL12]. parameters [Ba97]. Paris [CGM95]. Particle [XGW13]. Patterns [Szy91]. payments [OC13]. Pendulum [BS93b, Vil14, CS08, Thu72]. Pennsylvania [Tra76]. perimeter [Sur00, WCJQ14]. period [CS08, Thu72]. périodes [BM88]. periods [BM88, CT13b, CT13a]. permissible [OC13]. Peter [Ask88, Ber88, Wim88]. Pi [Ask88, BB16a, BBB97, BBB00, BBB04, BB87, Bor89, BB98, Bre17, Bre20, AAS16, BBB16, CL92, Kan16, Sin16, Ber88, Cas99, Wim88]. Picard [KS07, KS08]. piece [Lin91]. Pittsburgh [Tra76]. plan [SA06]. plane [Fou99]. point [Eng06]. Points [Gau02]. polylogarithmic [BBP16]. polynomial [Eng06, JK99, Wil63]. polynomials [GM17]. pondered [Ben95]. Popoviciu [Mih05]. population [Aiy45]. Positive [Als00, And83, CN87, GQ03, Has14, KL07, KLL09, Opp65, Opp68, Qi03a, Qi03b, RLC09, ST94, Vas72, Xue17, Yam13, ZC15]. postulates [Hun27]. power [Bur16, Xu15, Yan14]. power-convexity [Xu15]. pp [Ber88]. Precision [Bre76a, Bre06, Krä93, LO96, Bol99, Bre75, Bre76b, Bre10a, Bre16, Kan88, Kan16, Kar93, Bol99]. presence [SA06]. present [Dis02]. preserve [Baj78]. previously [BBMW16]. Price [Ber88]. prime [Has13b]. probability [YYC08]. problem [DJ94, Eve67, Eve69]. Problems [MP88]. procedure [MH72]. Proceedings [Bro96, Tra76, AFL96, ML88, CGM95]. process [CO17, OC13]. Product [Osl15, Wu05]. production [Cha14, CO17, OC13]. production-inventory [Cha14]. Products [Hor95, FKY09, IKW16, Mat93, Mat95a]. program [Bro96, Kan88, Kan16]. Programming [Pas71, dal96]. Proof [Ake63, Als00, BS93a, Cus81, Dia60, Gen18, GT20, Ked94, Mat10, Nel87, Nel95, Nel15, Saw17, Sch86, Sch78, Sch82, Abr79, Alz96, BS12, Ben93, Ben94, Ben95, Ben98, Cho76, Dob01, Lan78, Mat95b, Mes23, PV97, Pla22, QS09, SM99, SK77, Shi11, Uch08, Yam13]. Proofs [BRT18, Haj20, Mur97]. properties [Nis15, NC90, Rau42]. propietati [Gau92]. propietatibusque [Gau17]. Prover [KP96a, KP96b]. pseudo [Alz92a, Mih05]. pseudo-arithmetic [Alz92a]. Puzzle [Kat03].

quadratic [GZCS16, QC14]. quadratically [BB86]. quantities [CB10b, LM70]. quartically [Bai16]. quasi [ZX11]. quasi-arithmetic [ZX11]. quotient [Xu15].

Radicals [Osl15]. radius [She16, She17]. Rado [Mih05]. Ramanujan [AB88, AB16, Bor03a, Bor03b, Bor03c, Bor04c, Bor04b, Bor04a, BCF04, BC04, BBB16, Gar94, Lor08]. Random [CL92, Gla76]. Rapid [Bol99, BBP16]. rapide [Bol99]. rates [RM92, Roy03]. Ratio [FAB12, PM82, Ald10, Gla76, GQ03, Has13b, HM86, LQ15, Lin91, Nan80, Qi03a, Qi03b]. real [Bor04c, BCF04]. real-parameter [BCF04]. rectangular [MH71]. Recursive [OC14]. Reduced [BB84c]. Reduction [MNR^{+}22]. Refined [ABK16, Mer03, KMS79]. refinement [Ald08, Alz89, Alz97, CF78, Fen95, Hao93, ZH15]. Refinements [Bak16, Dra93a, Dra93b, FT08]. Related [Kos98, Toa98, AMPV97, BE15, CS17, Ito08, LL11, Naj13, OC14, PM97, She17, WY88]. relating [Nan46]. relationship [CE09, DJ94]. reliability [SA06]. Renormalizing [BS93b]. Research [Xu15]. respect [ZX11]. Result [Krä93, AK93, Kar93]. results [Naj13, SZ13, Tao06, Wu05]. reverse [Xue17, ZFFS14, ZC15]. reversed [Bak16]. Review [Ber88, Cas99, MNC71, TBDS92, Wim88]. Reviews [Ask88]. Revisited [BLM96, BLM97, Min87, BK08]. Revisiting [Jam18]. rework [CO17]. Riemannian [IP17, Yam13]. Roger [Mal98]. Root [Nel87, Nel89, Hun27]. root-mean-square [Hun27].

Salamin [New85, New16]. sample [Gla76, Lin91]. samples [Nan80]. sampling [Sen87]. Sándor [QCZ15]. scale [FLFJ11]. SCAN [AFL96]. SCAN-95 [AFL96]. Schur [Xu15]. Schur- [Xu15]. Schwarz [Aud15, ZJ16]. Science [Tra76]. Scientific [AK93, AFL96]. search [IP17]. Second [Wan99, CQWZ15, Rau42]. sector [LL11]. Seiffert [CZW11, CWQ12, CQWZ15, GSWC12, LGSC13, Yan14]. Self [Ald09, FLFJ11]. self-consistent [FLFJ11]. Self-improvement [Ald09]. September [AFL96, BBB^{+}20]. sequence [GQ03, Mar88, Qi03a, Qi03b]. Sequences [Sch84, Her72]. Series [Ber88, Xie02, HM86, KM12, KM13, Rau42]. set [FLFJ11]. set-averaging [FLFJ11]. Sets [Hun27, Opp65, Opp68, Vas72]. Sharp [Ald12, CWQM13, GZCS16, LGSC13, QCZ15, WCW11, WCW12, YSC14, Yan14, GSWC12, KLL09, LQ15]. sharpening [Alz92b, Peč95, Wu05]. Sharpenings [Alz90e]. short [Mur97]. should [Mal98]. Simple [BS93b, Dia60, Vil14, CB10b, CS08, Thu72, Uch08]. simplified [New85, New16]. simulation [FAB12]. Singular [Alb12, GHT11, Hir16, Rua15, Tao06, Zou17]. size [CO17]. Society [Ber88]. Solution [Zul86, Chu12]. Some [Alz99, Ba97, BRT18, Bul67, CB10b, Kin21, Kit99, Mit70, Naj13, SZ13, Toa98, Wil63, Wu05, YYC08, DCP97, FT08, Kit94, LL11]. source [BBB97, BBB00, BBB04]. sourcebook [BB16a]. space [KKLP12, ZC15]. spaces [Mar88]. Special [Baj78, Alz94, Bre10b, Tri66]. spectra [ZFFS14]. Square [Nel87, Nel89, Hun27]. Square-Arithmetic [Nel89]. SST [Gau02]. starlike [SMY14]. statistical [Tan06]. Still [Sch82]. stochastic [DJ94]. Structure [Car11, Nis88, Nis94]. Study [Ber88, BB87, Bro96, KP96a, Wim88, BB98, KP96b]. sua [Tri65]. subordinations [CK13, LL11]. subpermanents [CE09]. sufficient [WZSC14]. Sull’algoritmo [Tri65]. Summation [Xie02]. Supercomputing [ML88]. supply [Cha14, Chu12]. survey [YYC08]. Swarms [GOST23]. Swedish [Alm78]. Symmetric [Gas97, Lek09, Mit70]. Symmetry [MNR^{+}22]. Symposium [AFL96, Tra76, CGM95]. system [Chu12]. systems [Nak01, SA06].

tables [YMT10]. Telescoping [Saw17]. tell [Sen87]. ten [AAS16]. term [KLS00]. terms [CQWZ15, DZ17, GZCS16, KS07, LGSC13, QC14, QCZ15, Yan14]. test [SA06]. Texts [Ber88]. their [Ba97, MV10, Tan06, Wac00]. Them [BRT18]. Theorem [KP96a, Sch88, Gas97, KP96b, Ono83, Had12]. Theorie [Gep28]. Theory [Ber88, BB87, But36, Car11, Wim88, Bel14, BB98, Gep28, XGW13]. thermodynamic [Abr79, Lan78]. thermodynamics [Wan99]. Theta [Car11]. Three [Als00, Kat03, Neu96, Sei97, IKW16, KLL09, KS07, Opp65, Opp68, RLC09, Shi11]. Toader [CW12, DZ17]. Trace [FKY09, LZ06, Yan00]. transformation [Nis15]. Transformations [Sal89]. transforming [Mol11]. transition [FLFJ11]. Treatise [Par65, Par68, Par79]. Trigonometric [Nel15, Xie02]. trillion [AAS16]. Turán [BRS13]. Tutorial [KP96a, KP96b]. Two [Dra93b, Cha14, CWQM13, Lin91, MV10, Mur97, Opp65, Opp68, Sei87, Vas72, Xue17, YMT10, Dra93a, MP88]. two-echelon [Cha14]. two-piece [Lin91]. two-way [YMT10]. type [Aiy45, BRS13, Mih05, YMT10].

uncertainty [YMT10]. Ungleichung [Alz87]. Ungleichungen [Alz88]. Unification [Zou19]. unit [Qi03a, Qi03b]. Unitarily [Hor95, Fur94, Zou19]. united [QS09]. Univalence [KL96, KL98, OT04, Baj78]. University [Tra76]. Unrestricted [Bre10b]. unweighted [Nan80]. Upper [ST94, ZFFS14, ABK16, Kno03, LQ15, Pin15, SZ13, Tun75]. use [Tri66, Zul86]. Using [KP96a, Sal76, Sal97, Sal00, Sal04, Bai16, Dob01, Dup11, FAB12, KP96b, Sal16, WCJQ14]. usual [Thu72].

validated [AFL96]. validity [Chu12]. Value [Sch88, Alb12, GHT11, Tao06]. Values [Toa98, Alz90f, Alz90a, Dis02, Har91, Hir16, Rua15, Zou17, Sei87]. variables [Liu94, MH72, Shi11]. Variance [Rod17]. varieties [MT10]. Various [HK99, BBP16]. Vectorization [Kan88, Kan16]. Verallgemeinerung [Hei81]. Verification [Krä93, AK93, Kar93]. version [Bha06, New85, New16, She16]. versions [FT08, FFSZ16]. versus [FLFJ11]. via [Eng06, Hof16, Mah20, Sal89, Sch88, Sch89, Yam06]. Visualization [BBB^{+}20]. Vuorinen [TBDS92].

way [YMT10]. Weibull [Roy03]. Weierstrass [Wu05]. Weighted [Hof16, Pas71, Alz90a, Ben94, Dra98, Fin81, Gao15, Hol06, KL07, KLL09, KLL11, MW12, Nan80, Xue17, Yam13, Yan14, Zul86]. weighted-arithmetic [Fin81]. well [Har91]. well-known [Har91]. Werke [Gau66, Gau11]. Werte [Sei87]. Wiley [Ber88]. Wisk. [Dra93a]. within [FLFJ11].

Without

[Nel15, Als00, Nel87, Nel95, Sch86]. Words [Als00, Nel87, Nel15, Sch86, Nel95]. work [Sch11]. Wuppertal [AFL96].

xv [Ber88].

Yau [MT10]. York [Ber88]. Young [Wu17]. youthful [Sch11].

Zahlen [Sei87]. zero [Bre76b, Bre10a]. zerofinding [Bre76b, Bre10a]. zeros [Her72]. zum [Sch11]. Zur [Gep28]. zweier [Sei87]. zwischen [Alz87, Sei87].

References

Agarwal:2016:BGC

[AAS16] Ravi Agarwal, Hans Agarwal, and Syamal Sen. Birth, growth and computation of pi to ten trillion digits (2013). In Bailey and Borwein [BB16a], pages 363–423. ISBN 3-319-32375-X, 3-319-32377-6 (e-book). LCCN QA251. URL http:/

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Aujla:2007:EIC

[AB07] Jaspal Singh Aujla and Jean-Christophe Bourin. Eigenvalue inequalities for convex and log-convex functions. Linear Algebra and its Applications, 424(1):25–35, 2007. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

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[AB16] Gert Almkvist and Bruce Berndt.

Gauss, Landen, Ramanujan, the arithmetic–geometric mean, ellipses, π, and the Ladies Diary (1988). In Bailey and Borwein [BB16a], pages 125– 150. ISBN 3-319-32375-X, 3-319-32377-6 (e-book). LCCN QA251.

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Alzer:1990:IAG

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Alzer:1990:LBD

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Alzer:1990:SAM

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Alzer:1990:GGA

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Alzer:1994:NSA

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Alzer:1996:PAM

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Arndt:2010:AEI

[Arn11a] Jörg Arndt. The AGM, elliptic integrals, and algorithms for computing π. In Matters Computational [Arn11b], pages 599– 621. ISBN 3-642-14764-X, 3-642-14763-1. LCCN QA9.58 .A76 2011.

Arndt:2011:MC

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[Bai16] David H. Bailey. The computation of π to 29,360,000 decimal digits using Borweins’ quartically convergent algorithm (1988). In Bailey and Borwein [BB16a], pages 109–124. ISBN 3-319-32375-X, 3-319-32377-6 (e-book). LCCN QA251. URL http:/

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[BB84b] J. M. Borwein and P. B. Borwein.

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[BB84c] J. M. Borwein and P. B. Borwein.

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Borwein:1986:MQC

[BB86] J. M. Borwein and P. B. Borwein. More quadratically converging algorithms for π. Mathematics of Computation, 46(173): 247–253, January 1986. CO-DEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic).

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Borwein:1987:PAS

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Borwein:1988:CCJ

[BB88] J. M. Borwein and P. B. Borwein. A cubic counterpart of Jacobi’s identity and the AGM. Report, Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, NS B3H 3J5, Canada, December 31, 1988. 20 pp.

Borwein:1989:MI

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Borwein:1993:ICM

[BB93] Jonathan M. Borwein and Peter B. Borwein. Inequalities for compound mean iterations with logarithmic asymptotes. Journal of Mathematical Analysis and Applications, 177(2):572– 582, 1993. CODEN JMANAK. ISSN 0022-247X (print), 1096-0813 (electronic). URL http:/

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[BB97] J. M. Borwein and P. B. Borwein. The arithmetic–geometric mean and fast computation of elementary functions. In Berggren et al. [BBB97], pages 537– 552. ISBN 0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0 (print), 3-540-94924-0. LCCN QA484 .P5 1997. URL http:/

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[BB98] Jonathan M. Borwein and Peter B. Borwein. Pi and the AGM: A study in analytic number theory and computational complexity. Canadian Mathematical Society Series of Monographs and Advanced Texts, 4. Wiley, New York, NY, USA, 1998. ISBN 0-471-31515-X. xvi + 414 pp. Reprint of the 1987 original.

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Bailey:2016:PNG

[BB16a] David H. Bailey and Jonathan M. Borwein, editors. Pi: the next generation: a sourcebook on the recent history of Pi and its computation. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2016. ISBN 3-319-32375-X, 3-319-32377-6 (e-book). xiv + 507 pp. LCCN QA251. URL http:/

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[BB16b] J. M. Borwein and P. B. Borwein. The arithmetic–geometric mean and fast computation of elementary functions (1984). In Bailey and Borwein [BB16a], pages 79–96. ISBN 3-319-32375-X, 3-319-32377-6 (e-book). LCCN QA251. URL http:/

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[BBB97] Lennart Berggren, Jonathan M.

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Berggren:2000:PSB

[BBB00] Lennart Berggren, Jonathan Borwein, and Peter Borwein, editors. Pi: a source book. Springer-Ver-lag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., second edition, 2000. ISBN 0-387-98946-3 (hardcover). xx + 736 pp. LCCN QA484 .P5 2000.

Berggren:2004:PSB

[BBB04] Lennart Berggren, Jonathan Borwein, and Peter Borwein, editors. Pi: a source book. Springer-Ver-lag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., third edition, 2004. ISBN 0-387-20571-3. xx + 797 pp.

Borwein:2016:RME

[BBB16] Jonathan M. Borwein, Peter B. Borwein, and David H. Bailey. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi (1989). In Bailey and Borwein [BB16a], pages 175–195. ISBN 3-319-32375-X, 3-319-32377-6 (e-book). LCCN QA251. URL http:/

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Bailey:2020:AVC

[BBB^{+}20] David H. Bailey, Naomi Simone Borwein, Richard P. Brent, Regina S. Burachik, Judy anne Heather Osborn, Brailey Sims, and Qiji J. Zhu, editors. From Analysis to Visualization: A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017, volume 313 of Springer Proceedings in Mathematics & Statistics. Springer-Ver-lag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2020. ISBN 3-030-36567-0 (print), 3-030-36568-9 (e-book). ISSN 2194-1009 (print), 2194-1017 (electronic). LCCN ????

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[Kan88] Yasumasa Kanada. Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of π calculation. In Martin and Lundstrom [ML88], pages 117–128. CODEN ???? ISBN 0-8186-0882-X (v. 1; paper), 0-8186-8882-3 (v. 1; case), 0-8186-4882-1 (v. 1: microfiche) 0-8186-8923-4 (v. 2), 0-8186-5923-X (v. 2: microfiche), 0-8186-8923-4 (v. 2: case). ISSN ???? LCCN QA76.5 .S894 1988. Two volumes. IEEE catalog number 88CH2617-9. IEEE Computer Society Order Number 882.

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[Kin21] Louis Vessot King. On some new formulae for the numerical calculation of the mutual induction of coaxial circles. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 100(702):60–66, October 4, 1921. ISSN 0950-1207 (print), 2053-9150 (electronic). URL http:/

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King:1924:DNC

[Kin24] Louis Vessot King. On the Direct Numerical Calculation of Elliptic Functions and Integrals. Cambridge University Press, Cambridge, UK, 1924. viii + 42 pp. LCCN QA343.

King:2007:DNC

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Kittaneh:1992:NAG

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Kittaneh:1994:SOI

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[KL98] S. Kanas and A. Lecko. Univalence criteria connected with arithmetic and geometric means. I. In Transform methods & special functions, Varna ’96, pages 201– 209. Bulgarian Acad. Sci., Sofia, 1998.

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[KL07] Sejong Kim and Yongdo Lim. A converse inequality of higher order weighted arithmetic and geometric means of positive definite operators. Linear Algebra and its Applications, 426(2–3): 490–496, October 15, 2007. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

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Kober:1958:AGM

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Kosaki:1998:AGM

[Kos98]  Hideki Kosaki.  Arithmetic–

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Optimal inequalities for generalized logarithmic, arithmetic, and geometric means. Journal of Inequalities and Applications, pages 806825:1–806825:10, 2010. ISSN 1025-5834.

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