std::riemann_zeta,std::riemann_zetaf,std::riemann_zetal (3) - Linux Manuals

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

NAME

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:

* For arg>1, Σ∞
  n=1n-arg
* For 0≤arg≤1,

  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.