Posted by David Galant on May 16, 1998 at 04:54:51:
In Reply to: Re: Gaussian quadrature weight of the form 1/(1+x^2) posted by juergen on March 30, 1998 at 10:09:28:
: : hi, I wonder if there is ready made program or
: : calculated abscissas and weights for the Gaussian
: : quadrature of the form W(x)=1/(1+x^2), please let
: : me know if you know one.
: two references which might be helping (I don't
: have them under my eyes so I can't guarantee)
: J Ma, V Rohklin, S Wandzura
: "Generalized gaussian quadrature rules for systems
: of arbitrary functions"
: SIAM J Num Ana, 33(3) 971-996, June 1996
: A Sidi
: "Numerical Quadrature Rules fro some infinite
: range integrals"
: Math Comp 38(157) 127-142, Jan 1982
TOMS algorithm 726 will allow you to generate weights and abcissas for this weight function.
The orthogonal polynomials associated with this weight function are non classical and are unknown. The only method I know for directly getting the three term recurrence relation parameters is numerically unstable.