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      std::ellint_1,std::ellint_1f,std::ellint_1l

      From cppreference.com
      <cpp‎ |numeric‎ |special functions
       
       
       
       
      Defined in header<cmath>
      (1)
      float       ellint_1(float k,float phi);

      double      ellint_1(double k,double phi);

      longdouble ellint_1(longdouble k,longdouble phi);
      		(since C++17)
      (until C++23)
      /* floating-point-type */ ellint_1(/* floating-point-type */ k,
                                         /* floating-point-type */ phi);
      		(since C++23)
      float       ellint_1f(float k,float phi);
      		 (2)(since C++17)
      longdouble ellint_1l(longdouble k,longdouble phi);
      		 (3)(since C++17)
      Defined in header<cmath>
      template<class Arithmetic1,class Arithmetic2>

      /* common-floating-point-type */

          ellint_1( Arithmetic1 k, Arithmetic2 phi);
      		 (A)(since C++17)
      1-3) Computes theincomplete elliptic integral of the first kind ofk andphi. The library provides overloads ofstd::ellint_1 for all cv-unqualified floating-point types as the type of the parametersk andphi.(since C++23)
      A) Additional overloads are provided for all other combinations of arithmetic types.

      Contents

      [edit]Parameters

      k - elliptic modulus or eccentricity (a floating-point or integer value)
      phi - Jacobi amplitude (a floating-point or integer value, measured in radians)

      [edit]Return value

      If no errors occur, value of the incomplete elliptic integral of the first kind ofk andphi, that is∫phi
      0
      dθ
      √1-k2
      sin2
      θ
      , is returned.

      [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.
      • If|k|>1, a domain error may occur.

      [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 also available inboost.math.

      The additional overloads are not required to be provided exactly as(A). They only need to be sufficient to ensure that for their first argumentnum1 and second argumentnum2:

      • Ifnum1 ornum2 has typelongdouble, thenstd::ellint_1(num1, num2) has the same effect asstd::ellint_1(static_cast<longdouble>(num1),
                     static_cast<longdouble>(num2))        .
      • Otherwise, ifnum1 and/ornum2 has typedouble or an integer type, thenstd::ellint_1(num1, num2) has the same effect asstd::ellint_1(static_cast<double>(num1),
                     static_cast<double>(num2))        .
      • Otherwise, ifnum1 ornum2 has typefloat, thenstd::ellint_1(num1, num2) has the same effect asstd::ellint_1(static_cast<float>(num1),
                     static_cast<float>(num2))        .
      		(until C++23)

      Ifnum1 andnum2 have arithmetic types, thenstd::ellint_1(num1, num2) has the same effect asstd::ellint_1(static_cast</* common-floating-point-type */>(num1),
                   static_cast</* common-floating-point-type */>(num2))      , where/* common-floating-point-type */ is the floating-point type with the greatestfloating-point conversion rank and greatestfloating-point conversion subrank between the types ofnum1 andnum2, arguments of integer type are considered to have the same floating-point conversion rank asdouble.

      If no such floating-point type with the greatest rank and subrank exists, thenoverload resolution does not result in a usable candidate from the overloads provided.

      		(since C++23)

      [edit]Example

      Run this code
      #include <cmath>#include <iostream>#include <numbers> int main(){constdouble hpi=std::numbers::pi/2.0; std::cout<<"F(0,π/2)  = "<< std::ellint_1(0, hpi)<<'\n'<<"F(0,-π/2) = "<< std::ellint_1(0,-hpi)<<'\n'<<"π/2       = "<< hpi<<'\n'<<"F(0.7,0)  = "<< std::ellint_1(0.7,0)<<'\n';}

      Output:

      F(0,π/2)  = 1.5708F(0,-π/2) = -1.5708π/2       = 1.5708F(0.7,0)  = 0

      [edit]See also

      (complete) elliptic integral of the first kind
      (function)[edit]

      [edit]External links

      Weisstein, Eric W. "Elliptic Integral of the First Kind." From MathWorld — A Wolfram Web Resource.
      Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/special_functions/ellint_1&oldid=149537"
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