std::riemann_zeta, std::riemann_zetaf, std::riemann_zetal

Header: <cmath>

1-3) Computes the Riemann zeta function of num.The library provides overloads of std::riemann_zeta for all cv-unqualified floating-point types as the type of the parameter num.(since C++23)

# Declarations

float riemann_zeta ( float num );
double riemann_zeta ( double num );
long double riemann_zeta ( long double num );

(since C++17) (until C++23)

/* floating-point-type */ riemann_zeta( /* floating-point-type */ num );

(since C++23)

float riemann_zetaf( float num );

(since C++17)

long double riemann_zetal( long double num );

(since C++17)

Additional overloads

template< class Integer >
double riemann_zeta ( Integer num );

(since C++17)

# Parameters

• num: floating-point or value

# Return value

If no errors occur, value of the Riemann zeta function of num, ζ(num), defined for the entire real axis:

# Notes

Implementations that do not support C++17, but support ISO 29124:2010, provide this function if STDCPP_MATH_SPEC_FUNCS is defined by the implementation to a value at least 201003L and if the user defines STDCPP_WANT_MATH_SPEC_FUNCS before including any standard library headers.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1.

An implementation of this function is also available in boost.math.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::riemann_zeta(num) has the same effect as std::riemann_zeta(static_cast(num)).

# Example

#include <cmath>
#include <format>
#include <iostream>
#include <numbers>
 
int main()
{
    constexpr auto π = std::numbers::pi;
 
    // spot checks for well-known values
    for (const double x : {-1.0, 0.0, 1.0, 0.5, 2.0})
        std::cout << std::format("ζ({})\t= {:+.5f}\n", x, std::riemann_zeta(x));
    std::cout << std::format("π²/6\t= {:+.5f}\n", π * π / 6);
}