bessel_i

auto eve::bessel_i = eve::functor<bessel_i_t>

inlineconstexpr

#include <eve/functions.hpp>

Callable Signatures

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

External references

• Wolfram MathWorld: Bessel Function of the Second Kind
• Wolfram MathWorld: Spherical Bessel Function of the Second Kind
• Wikipedia: Bessel function
• DLMF: 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_j(wu, wdf)                = " << eve::bessel_j(wu, wdf) << "\n";
   std::cout << "-> bessel_j[ignore_last(2)](wu, wdf)= " << eve::bessel_j[eve::ignore_last(2)](wu, wdf) << "\n";
   std::cout << "-> bessel_j[wu != 2u](wu, wdf)      = " << eve::bessel_j[wu != 2u](wu, wdf) << "\n";
   std::cout << "-> bessel_j(m, wd)                  = " << eve::bessel_j(m, wd) << "\n";
   std::cout << "-> bessel_j[spherical](m, wd)       = " << eve::bessel_j[eve::spherical](m, wd) << "\n";
}