Lattice Builder Manual Software Package for Constructing Rank-1 Lattices

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LatBuilder::Functor::BernoulliPoly< DEGREE > Struct Template Reference

Bernoulli polynomial. More...

`#include <BernoulliPoly.h>`

## Detailed Description

### template<unsigned int DEGREE>
struct LatBuilder::Functor::BernoulliPoly< DEGREE >

Bernoulli polynomial.

The first few Bernoulli polynomials:

\begin{eqnarray*} B_0(x) &=& 1 \\ B_1(x) &=& x - 1/2 \\ B_2(x) &=& x^2 - x + 1/6 \\ B_3(x) &=& x^3 - 3x^2/2 + x/2 \\ B_4(x) &=& x^4 - 2x^3 + x^2 - 1/30 \\ B_5(x) &=& x^5 - 5x^4/2 + 5x^3/3 - x/6 \\ B_6(x) &=& x^6 - 3x^5 + 5x^4/2 - x^2/2 + 1/42 \\ B_8(x) &=& x^8 - 4x^7 + 14x^6/3 - 7x^4/3 + 2x^2/3 - 1/30. \end{eqnarray*}

where \(B_{2\alpha}(x)\) is the Bernoulli polynomial of degree \(2\alpha\).

Template Parameters

  DEGREE | Degree of the polynomial.

Remarks
  Specializations are implemented up to degree 8.

The documentation for this struct was generated from the following file:

- latbuilder/include/latbuilder/Functor/BernoulliPoly.h