E.V.E
v2022.09.01

◆ cyl_bessel_j1

eve::cyl_bessel_j1 = {}
inlineconstexpr

Computes the Bessel function of the first kind, \( J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )\,\mathrm {d} \tau \).

It is the solution of \( x^{2}y''+xy'+(x^2-1)y=0\) for which \( y(0) = 0\).

Defined in header

#include <eve/module/bessel.hpp>

Callable Signatures

namespace eve
{
template< eve::floating_real_value T >
T cyl_bessel_j1(T x) noexcept;
}
constexpr callable_cyl_bessel_j1_ cyl_bessel_j1
Computes the Bessel function of the first kind, .
Definition: cyl_bessel_j1.hpp:53
Definition: all_of.hpp:22

Parameters

Return value

The value of \( \displaystyle J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau ) \,\mathrm {d} \tau \) is returned.

Example

#include <eve/module/bessel.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
#include <eve/module/core.hpp>
wide_ft x = {0.5, 1.5, 0.1, 1.0, 19.0, 25.0, 21.5, 10000.0};
std::cout << "---- simd" << '\n'
<< "<- x = " << x << '\n'
<< "-> cyl_bessel_j1(x) = " << eve::cyl_bessel_j1(x) << '\n'
;
double xd = 1.0;
std::cout << "---- scalar" << '\n'
<< "<- xd = " << xd << '\n'
<< "-> cyl_bessel_j1(xd) = " << eve::cyl_bessel_j1(xd) << '\n';
return 0;
}
Wrapper for SIMD registers.
Definition: wide.hpp:65