Num.h File Reference

This module implements a few useful mathematical functions. More...

#include <cstdint>

Namespaces
	LatticeTester
	Lattice namespace.

Functions
std::int64_t	LatticeTester::lFactorial (int t)
	Calculates \(t!\), the factorial of \(t\).
double	LatticeTester::Digamma (double x)
	Returns the value of the logarithmic derivative of the Gamma function \(\psi(x) = \Gamma'(x) / \Gamma(x)\).
double	LatticeTester::BernoulliPoly (int n, double x)
	Evaluates the Bernoulli polynomial \(B_n(x)\) of degree \(n\) at \(x\). More...
double	LatticeTester::Harmonic (std::int64_t n)
	Computes the \(n\)-th harmonic number \(H_n = \sum_{j=1}^n 1/j\).
double	LatticeTester::Harmonic2 (std::int64_t n)
	Computes the sum \[ \sideset{}{'}\sum_{-n/2<j\le n/2}\; \frac 1{|j|}, \] where the symbol \(\sum^\prime\) means that the term with \(j=0\) is excluded from the sum.
double	LatticeTester::FourierC1 (double x, std::int64_t n)
	Computes and returns the value of the series (see [15]) \[ S(x, n) = \sum_{j=1}^{n} \frac{\cos(2\pi j x)}{j}. \] Restrictions: \(n>0\) and \(0 \le x \le 1\).
double	LatticeTester::FourierE1 (double x, std::int64_t n)
	Computes and returns the value of the series \[ G(x, n) = \sideset{}{'}\sum_{-n/2<h\le n/2}\; \frac{e^{2\pi i h x}}{|h|}, \] where the symbol \(\sum^\prime\) means that the term with \(h=0\) is excluded from the sum, and assuming that the imaginary part of \(G(x, n)\) vanishes. More...

Detailed Description

This module implements a few useful mathematical functions.