E.V.E
v2022.09.01

◆ airy_bi

eve::airy_bi = {}
inlineconstexpr

Computes the airy function \( Bi(x)\).

It is the solution of the differential equation \(y''-xy = 0\) satisfying \(Ai(0) = \frac1{3^{1/6}\Gamma(2/3)}\) and \(Ai'(0) =\frac{3^{1/6}}{\Gamma(1/3)}\).

Defined in header

#include <eve/module/bessel.hpp>

Callable Signatures

namespace eve
{
template< eve::floating_real_value T >
T airy_bi(T x) noexcept;
}
constexpr callable_airy_bi_ airy_bi
Computes the airy function .
Definition: airy_bi.hpp:57
Definition: all_of.hpp:22

Parameters

Return value

The value of \( \displaystyle Bi(x) = \frac1{\pi}\int_{0}^{\infty} \left[\exp\left(-{\frac{t^{3}}{3}}+xt\right)+ \sin\left({\frac{t^{3}}{3}}+xt\right)\,\right]dt\) is returned.

Example

#include <eve/module/bessel.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft pf = {0.5, -1.5, 0.1, -1.0, 19.0, 25.0, 21.5, 10.0};
std::cout << "---- simd" << '\n'
<< "<- pf = " << pf << '\n'
<< "-> airy_bi(pf) = " << eve::airy_bi(pf) << '\n'
;
double xd = -1.0;
std::cout << "---- scalar" << '\n'
<< "<- xd = " << xd << '\n'
<< "-> airy_bi(xd) = " << eve::airy_bi(xd) << '\n';
return 0;
}
Wrapper for SIMD registers.
Definition: wide.hpp:65