Std::riemann_zeta,std::riemann_zetaf,std::riemann_zetal (3) Linux Manual Page

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

Synopsis

double riemann_zeta( double arg );

float riemann_zeta( float arg );

long double riemann_zeta( long double arg );  (1) (since C++17)

float riemann_zetaf( float arg );

long double riemann_zetal( long double arg );

double riemann_zeta( IntegralType arg );      (2) (since C++17)

1) Computes the Riemann_zeta_function of arg.
2) A set of overloads or a function template accepting an argument of any integral_type. Equivalent to (1) after casting the argument to double.

Parameters

arg – value of a floating-point or integral type

Return value

If no errors occur, value of the Riemann zeta function of arg, ζ(arg), defined for the entire real axis:
1
1-21-arg

Σ∞

n=1(-1)n-1

n-arg

* For arg<0, 2arg

πarg-1

sin(

  πarg
  2
  )Γ(1−arg)ζ(1−arg)

Error handling

Errors may be reported as specified in math_errhandling

* If the argument is NaN, NaN is returned and domain error is not reported

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

Example

// Run this code

#include <cmath>

#include <iostream>

int main()

{
    // spot checks for well-known values
    std::cout << "ζ(-1) = " << std::riemann_zeta(-1) << '\n'
              << "ζ(0) = " << std::riemann_zeta(0) << '\n'
              << "ζ(1) = " << std::riemann_zeta(1) << '\n'
              << "ζ(0.5) = " << std::riemann_zeta(0.5) << '\n'
              << "ζ(2) = " << std::riemann_zeta(2) << ' '
              << "(π²/6 = " << std::pow(std::acos(-1), 2) / 6 << ")\n";
}

Output:

  ζ(-1) = -0.0833333
  ζ(0) = -0.5
  ζ(1) = inf
  ζ(0.5) = -1.46035
  ζ(2) = 1.64493 (π²/6 = 1.64493)

External links

Weisstein,_Eric_W._"Riemann_Zeta_Function." From MathWorld–A Wolfram Web Resource.

std::riemann_zeta,std::riemann_zetaf,std::riemann_zetal (3) Linux Manual Page