E.V.E
v2023.02.15
 
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◆ cyl_bessel_y1

auto eve::cyl_bessel_y1 = functor<cyl_bessel_y1_t>
inlineconstexpr

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

Header file

#include <eve/module/bessel.hpp>

Callable Signatures

namespace eve
{
// Regular overload
constexpr auto cyl_bessel_y1(floating_value auto x) -> decltype(x) noexcept; // 1
// Lanes masking
constexpr auto cyl_bessel_y1[conditional_expr auto c](floating_value auto x) noexcept; // 2
constexpr auto cyl_bessel_y1[logical_value auto m](floating_value auto x) noexcept; // 2
}
Specifies that a type is a Conditional Expression.
Definition conditional.hpp:28
The concept floating_value<T> is satisfied if and only if T satisfies eve::value and the element type...
Definition value.hpp:116
The concept logical_value<T> is satisfied if and only if T satisfies eve::value and the element type ...
Definition value.hpp:132
constexpr auto cyl_bessel_y1
elementwise_callable object computing the Bessel function of the second kind, .
Definition cyl_bessel_y1.hpp:76
EVE Main Namespace.
Definition abi.hpp:18

Parameters

Return value

  1. The value of \(\displaystyle Y_1(x)=\frac2{\pi}\int_{1}^{\infty}\frac{\cos x\tau} {(\tau^2-1)^{3/2}}\,\mathrm{d}\tau\) is returned.
  2. The operation is performed conditionnaly.

External references

Example

// revision 1
#include <eve/module/bessel.hpp>
#include <iostream>
eve::wide<double> wf0([](auto i, auto c)->double{ return 2*(i+c/2);});
eve::wide wf1{-0.5, 1.5, 0.1, 1.0, 19.0, 25.0, 21.5, 10000.0};
int main()
{
std::cout << "<- wf0 = " << wf0 << "\n";
std::cout << "<- wf1 = " << wf1 << "\n";
std::cout << "-> cyl_bessel_y1(wf0) = " << eve::cyl_bessel_y1(wf0) << "\n";
std::cout << "-> cyl_bessel_y1[ignore_last(2)](wf0)= " << eve::cyl_bessel_y1[eve::ignore_last(2)](wf0) << "\n";
std::cout << "-> cyl_bessel_y1[wf0!= -2.0f](wf0) = " << eve::cyl_bessel_y1[wf0!= -2.0f](wf0) << "\n";
std::cout << "-> cyl_bessel_y1(wf1) = " << eve::cyl_bessel_y1(wf1) << "\n";
}
Conditional expression ignoring the k last lanes from a eve::simd_value.
Definition conditional.hpp:332
Wrapper for SIMD registers.
Definition wide.hpp:70