sph_bessel_yn

eve::sph_bessel_yn = functor<sph_bessel_yn_t>

inlineconstexpr

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

Header file

#include <eve/module/bessel.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   template<value  N, floating_value T> constexpr as_wide_as_t<T,N> cyl_bessel_yn(N n, T x)   noexcept; // 1
 
   // Lanes masking
   constexpr auto sph_bessel_yn[conditional_expr auto c](value auto n, floating_value auto x) noexcept; // 2
   constexpr auto sph_bessel_yn[logical_value auto m](value auto n, floating_value auto x)    noexcept; // 2
}

Parameters

• n: Order of the function.
• x: Floating argument.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

The value of \( \displaystyle y_{n}(x)= (-x)^n\left(\frac1x\frac{d}{dx}\right)^n \frac{\cos x}x\) is returned.

External references

• Wikipedia: Spherical Bessel Functions
• Wolfram Mathwold: Spherical Bessel Function of the Second Kind
• DLMF: Spherical Bessel Functions

Example

// revision 1
#include <eve/module/bessel.hpp>
#include <iostream>
 
eve::wide<double> wf([](auto i, auto c)->double{ return 2*(i+c/2);});
eve::wide<std::uint64_t> wu([](auto i, auto )->std::uint64_t{ return 2*i;});
eve::wide x{0.5, 1.5, 0.1, 1.0, 19.0, 25.0, 21.5, 10000.0};
eve::wide n{0, 1, 15, 2, 25, 26, 3, 12};
 
int main()
{
   std::cout << "<- wf = " << wf << "\n";
   std::cout << "<- wu = " << wu << "\n";
   std::cout << "<- n  = " << n << "\n";
   std::cout << "<- x  = " << x << "\n";
 
   std::cout << "-> sph_bessel_yn(wu, wf)                = " << eve::sph_bessel_yn(wu, wf) << "\n";
   std::cout << "-> sph_bessel_yn[ignore_last(2)](wu, wf)= " << eve::sph_bessel_yn[eve::ignore_last(2)](wu, wf) << "\n";
   std::cout << "-> sph_bessel_yn[wu != 2u](wu, wf)      = " << eve::sph_bessel_yn[wu != 2u](wu, wf) << "\n";
   std::cout << "-> sph_bessel_yn(n, x)                  = " << eve::sph_bessel_yn(n, x) << "\n";
}