double cyl_bessel_i( double ν, double x ); float cyl_bessel_if( float ν, float x ); long double cyl_bessel_il( long double ν, long double x ); | (1) | (since C++17) |

Promoted cyl_bessel_i( Arithmetic ν, Arithmetic x ); | (2) | (since C++17) |

2) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1). If any argument has integral type, it is cast to

`double`

. If any argument is `long double`

, then the return type `Promoted`

is also `long double`

, otherwise the return type is always `double`

.ν | - | the order of the function |

x | - | the argument of the function) |

`ν`

and `x`

, that is Iν(x) = Σ∞

k=0

(x/2)ν+2k |

k!Γ(ν+k+1) |

Errors may be reported as specified in math_errhandling.

- If the argument is NaN, NaN is returned and domain error is not reported
- If ν>=128, the behavior is implementation-defined

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.

#include <cmath> #include <iostream> int main() { // spot check for ν == 0 double x = 1.2345; std::cout << "I_0(" << x << ") = " << std::cyl_bessel_i(0, x) << '\n'; // series expansion for I_0 double 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) = 1.41886 sum = 1 sum = 1.381 sum = 1.41729 sum = 1.41882 sum = 1.41886

Weisstein, Eric W. "Modified Bessel Function of the First Kind." From MathWorld--A Wolfram Web Resource.

(C++17)(C++17)(C++17) | cylindrical Bessel functions (of the first kind) (function) |

© cppreference.com

Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.

http://en.cppreference.com/w/cpp/numeric/special_math/cyl_bessel_i