std::cyl_bessel_j, std::cyl_bessel_jf, std::cyl_bessel_jl
Defined in header <cmath>
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(1) | ||
float cyl_bessel_j ( float nu, float x ); double cyl_bessel_j ( double nu, double x ); |
(since C++17) (until C++23) |
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/* floating-point-type */ cy_bessel_j( /* floating-point-type */ nu, /* floating-point-type */ x ); |
(since C++23) | |
float cyl_bessel_jf( float nu, float x ); |
(2) | (since C++17) |
long double cyl_bessel_jl( 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_j
for all cv-unqualified floating-point types as the type of the parameters nu and x. (since C++23)Parameters
nu | - | the order of the function |
x | - | the argument of the function |
Return value
If no errors occur, value of the cylindrical Bessel function of the first kind of nu and x, that is Jnu(x) = Σ∞
k=0
(-1)k (x/2)nu+2k |
k!Γ(nu+k+1) |
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.
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_j(num1, num2) has the same effect as std::cyl_bessel_j(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) |
Example
#include <cmath> #include <iostream> int main() { // spot check for nu == 0 const double x = 1.2345; std::cout << "J_0(" << x << ") = " << std::cyl_bessel_j(0, x) << '\n'; // series expansion for J_0 double fct = 1; double sum = 0; for (int k = 0; k < 6; fct *= ++k) { sum += std::pow(-1, k) * std::pow(x / 2, 2 * k) / std::pow(fct, 2); std::cout << "sum = " << sum << '\n'; } }
Output:
J_0(1.2345) = 0.653792 sum = 1 sum = 0.619002 sum = 0.655292 sum = 0.653756 sum = 0.653793 sum = 0.653792
See also
(C++17)(C++17)(C++17) |
regular modified cylindrical Bessel functions (function) |
External links
Weisstein, Eric W. "Bessel Function of the First Kind." From MathWorld — A Wolfram Web Resource. |