Std::cyl_bessel_i,std::cyl_bessel_if,std::cyl_bessel_il (3) Linux Manual Page

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

Synopsis

double cyl_bessel_i( double ν, double x );

float cyl_bessel_if( float ν, float x );                  (1) (since C++17)

long double cyl_bessel_il( long double ν, long double x );

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

1) Computes the regular_modified_cylindrical_Bessel_function of ν and x.
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.

Parameters

ν- the order of the function
x – the argument of the function)

Return value

If no errors occur, value of the regular modified cylindrical Bessel function of ν and x, that is I
ν(x) = Σ∞
k=0
(x/2)ν+2k
k!Γ(ν+k+1)
(for x≥0), is returned.

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
* If ν>=128, the behavior is implementation-defined

Notes

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

Example

// Run this code

#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

External links

Weisstein,_Eric_W._"Modified_Bessel_Function_of_the_First_Kind." From MathWorld–A Wolfram Web Resource.

std::cyl_bessel_i,std::cyl_bessel_if,std::cyl_bessel_il (3) Linux Manual Page