Lattice Builder Manual
Software Package for Constructing Rank-1 Lattices
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
DEGREEDegree of the polynomial.
Remarks
Specializations are implemented up to degree 8.

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