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

      From cppreference.com
      <cpp‎ |numeric‎ |special functions
       
       
       
       
      Defined in header<cmath>
      (1)
      float       riemann_zeta(float num);

      double      riemann_zeta(double num);

      longdouble riemann_zeta(longdouble num);
      		(since C++17)
      (until C++23)
      /* floating-point-type */ riemann_zeta(/* floating-point-type */ num);
      		(since C++23)
      float       riemann_zetaf(float num);
      		 (2)(since C++17)
      longdouble riemann_zetal(longdouble num);
      		 (3)(since C++17)
      Defined in header<cmath>
      template<class Integer>
      double      riemann_zeta( Integer num);
      		 (A)(since C++17)
      1-3) Computes theRiemann zeta function ofnum. The library provides overloads ofstd::riemann_zeta for all cv-unqualified floating-point types as the type of the parameternum.(since C++23)
      A) Additional overloads are provided for all integer types, which are treated asdouble.

      Contents

      [edit]Parameters

      num - floating-point or value

      [edit]Return value

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

      • Fornum>1,Σ∞
        n=1        n-num
      • For0≤num≤1,
        1
        21-num
        -1
        Σ∞
        n=1         (-1)n
         n-num
      • Fornum<0,2num
        πnum-1
        sin(
        πnum
        2
        )Γ(1−num)ζ(1−num)

      [edit]Error handling

      Errors may be reported as specified inmath_errhandling.

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

      [edit]Notes

      Implementations that do not support C++17, but supportISO 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 headertr1/cmath and namespacestd::tr1.

      An implementation of this function is alsoavailable 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 argumentnum of integer type,std::riemann_zeta(num) has the same effect asstd::riemann_zeta(static_cast<double>(num)).

      [edit]Example

      Run this code
      #include <cmath>#include <format>#include <iostream>#include <numbers> int main(){constexprauto π=std::numbers::pi; // spot checks for well-known valuesfor(constdouble 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);}

      Output:

      ζ(-1)   = -0.08333ζ(0)    = -0.50000ζ(1)    = +infζ(0.5)  = -1.46035ζ(2)    = +1.64493π²/6    = +1.64493

      [edit]External links

      Weisstein, Eric W. "Riemann Zeta Function." From MathWorld — A Wolfram Web Resource.
      Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/special_functions/riemann_zeta&oldid=158821"
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