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      std::cyl_bessel_i,std::cyl_bessel_if,std::cyl_bessel_il

      From cppreference.com
      <cpp‎ |numeric‎ |special functions
       
       
       
       
      Defined in header<cmath>
      (1)
      float       cyl_bessel_i(float nu,float x);

      double      cyl_bessel_i(double nu,double x);

      longdouble cyl_bessel_i(longdouble nu,longdouble x);
      		(since C++17)
      (until C++23)
      /* floating-point-type */ cyl_bessel_i(/* floating-point-type */ nu,
                                             /* floating-point-type */ x);
      		(since C++23)
      float       cyl_bessel_if(float nu,float x);
      		 (2)(since C++17)
      longdouble cyl_bessel_il(longdouble nu,longdouble x);
      		 (3)(since C++17)
      Defined in header<cmath>
      template<class Arithmetic1,class Arithmetic2>

      /* common-floating-point-type */

          cyl_bessel_i( Arithmetic1 nu, Arithmetic2 x);
      		 (A)(since C++17)
      1-3) Computes theregular modified cylindrical Bessel function ofnu andx. The library provides overloads ofstd::cyl_bessel_i for all cv-unqualified floating-point types as the type of the parametersnu andx.(since C++23)
      A) Additional overloads are provided for all other combinations of arithmetic types.

      Contents

      [edit]Parameters

      nu - the order of the function
      x - the argument of the function

      [edit]Return value

      If no errors occur, value of the regular modified cylindrical Bessel function ofnu andx, that isInu(x) = Σ∞
      k=0
      (x/2)nu+2k
      k!Γ(nu+k+1)
       (forx≥0), 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.
      • Ifnu≥128, the behavior is implementation-defined.

      [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 first argumentnum1 and second argumentnum2:

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

      Ifnum1 andnum2 have arithmetic types, thenstd::cyl_bessel_i(num1, num2) has the same effect asstd::cyl_bessel_i(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> int main(){// spot check for nu == 0constdouble x=1.2345;std::cout<<"I_0("<< x<<") = "<< std::cyl_bessel_i(0, x)<<'\n'; // series expansion for I_0double fct=1;double sum=0;for(int k=0; k<5; fct*=++k){        sum+=std::pow(x/2,2* k)/std::pow(fct,2);std::cout<<"sum = "<< sum<<'\n';}}

      Output:

      I_0(1.2345) = 1.41886sum = 1sum = 1.381sum = 1.41729sum = 1.41882sum = 1.41886

      [edit]See also

      cylindrical Bessel functions (of the first kind)
      (function)[edit]

      [edit]External links

      Weisstein, Eric W. "Modified Bessel Function of the First Kind." From MathWorld — A Wolfram Web Resource.
      Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/special_functions/cyl_bessel_i&oldid=149507"
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