std::riemann_zeta, std::riemann_zetaf, std::riemann_zetal
double riemann_zeta( float arg );
double riemann_zeta( long double arg );
float riemann_zetaf( float arg );
As all special functions, riemann_zeta is only guaranteed to be available in <cmath> 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.
[edit] Parameters
[edit] 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, 11 - 21-argΣ∞
n=1(-1)n-1
n-arg
. - For arg < 0, 2arg
πarg-1
sin(πarg2)Γ(1 − arg)ζ(1 − arg).
[edit] 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.
[edit] Notes
Implementations that do not support TR 29124 but support TR 19768, provide this function in the header tr1/cmath and namespace std::tr1.
An implementation of this function is also available in boost.math.
[edit] Example
(works as shown with gcc 6.0)
#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1 #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)
[edit] External links
Weisstein, Eric W. "Riemann Zeta Function." From MathWorld--A Wolfram Web Resource.