std::cyl_bessel_i, std::cyl_bessel_if, std::cyl_bessel_il
Defined in header <cmath>
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(1) | ||
float cyl_bessel_i ( float nu, float x ); double cyl_bessel_i ( double nu, double x ); |
(since C++17) (until C++23) |
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/* 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) |
long double cyl_bessel_il( long double nu, long double x ); |
(3) | (since C++17) |
Defined in header <cmath>
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template< class Arithmetic1, class Arithmetic2 > /* common-floating-point-type */ |
(A) | (since C++17) |
std::cyl_bessel_i
for all cv-unqualified floating-point types as the type of the parameters nu and x.(since C++23)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 of nu and x, that is Inu(x) = Σ∞k=0
(x/2)nu+2k |
k!Γ(nu+k+1) |
[edit] 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 nu≥128, the behavior is implementation-defined.
[edit] 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.
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1 and second argument num2:
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(until C++23) |
If num1 and num2 have arithmetic types, then std::cyl_bessel_i(num1, num2) has the same effect as std::cyl_bessel_i(static_cast</* common-floating-point-type */>(num1), If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided. |
(since C++23) |
[edit] Example
#include <cmath> #include <iostream> int main() { // spot check for nu == 0 const 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
[edit] See also
(C++17)(C++17)(C++17) |
cylindrical Bessel functions (of the first kind) (function) |
[edit] External links
Weisstein, Eric W. "Modified Bessel Function of the First Kind." From MathWorld — A Wolfram Web Resource. |