bessel_k

auto eve::bessel_k = eve::functor<bessel_k_t>

inlineconstexpr

#include <eve/functions.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto bessel_k(value auto n, floating_value auto z)                  noexcept; // 1
 
   // Semantic modifier
   constexpr auto bessel_k[cylindrical](value auto n, floating_value auto z)     noexcept; // 1
   constexpr auto bessel_k[spherical](value auto n, floating_value auto z)       noexcept; // 2
 
   // Lanes masking
   constexpr auto bessel_k[conditional_expr auto c](/*any previous overload*/)   noexcept; // 3
   constexpr auto bessel_k[logical_value auto m](/*any previous overload*/)      noexcept; // 3
}

Parameters

• n: order (integral or floating)
• z: Value to process.
• m: Logical value masking the operation.

Return value

1. returns \(Y_n\)(z) (cylindrical).
2. returns \(y_n\)(z) (spherical).
3. The operation is performed conditionally.

Note

if n is not integral nor flint negative z entries produce NaN outputs as the correct result is not real. You may want to use KYOSU to avoid this behavior and produce complex outputs (that are not available in EVE).

External references

• Wolfram MathWorld: Modified Bessel Function of the second Kind
• Wolfram MathWorld: Modified Spherical Bessel Function of the second Kind
• Wikipedia: Bessel function
• DLMF: Modified Bessel functions

Example

// revision 1
#include <eve/module/bessel.hpp>
#include <iostream>
 
eve::wide<double> wdf([](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 wd{0.5, 1.5, 0.1, 1.0, 19.0, 0.0, 0.0, 10000.0};
eve::wide m{0.5, -1.0, 1.5, -2.0, 2.5, -2.6, 3.2, -12.0};
 
int main()
{
   std::cout << "<- wdf = " << wdf << "\n";
   std::cout << "<- wu = " << wu << "\n";
   std::cout << "<- m  = " << m << "\n";
   std::cout << "<- wd  = " << wd << "\n";
 
   std::cout << "-> bessel_k(wu, wdf)                = " << eve::bessel_k(wu, wdf) << "\n";
   std::cout << "-> bessel_k[ignore_last(2)](wu, wdf)= " << eve::bessel_k[eve::ignore_last(2)](wu, wdf) << "\n";
   std::cout << "-> bessel_k[wu != 2u](wu, wdf)      = " << eve::bessel_k[wu != 2u](wu, wdf) << "\n";
   std::cout << "-> bessel_k(m, wd)                  = " << eve::bessel_k(m, wd) << "\n";
   std::cout << "-> bessel_k[spherical](m, wd)       = " << eve::bessel_k[eve::spherical](m, wd) << "\n";
}