gegenbauer

auto kyosu::gegenbauer = eve::functor<gegenbauer_t>

inlineconstexpr

Computes the value of the Gegenbauer function of order \(n\).

Computes the value of the Gegenbauer function of order \(n\) and parameter \(\lambda\), \(C^{(\lambda)}_n(z)\) at z. If \(n\) is an integer, the function is a polynomial of degree \(n\).

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   auto constexpr gegenbauer( auto n, auto lambda, auto z)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto gegenbauer[conditional_expr auto c](/* any previous overload */)  noexcept; // 2
   constexpr auto gegenbauer[logical_value auto m](/* any previous overload */)     noexcept; // 2
}

Parameters

• n, lambda, z : real or cayley_dickson.

Return value

1.The value of the function at z is returned. real input z is treated as complex(z).

1. The operation is performed conditionnaly.

External references

• Wolfram MathWorld: GegenbauerC
• Wikipedia: Gegenbauer polynomials
• DLMF: Gegenbauer Function

Example

// revision 1
#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  eve::wide xd{0.5, -1.5, 0.1, -1.0, 19.0, 25.0, 21.5, 10000.0};
  eve::wide n{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0};
  eve::wide l{-4.3, -1.0, -0.52, 3.2, 4.3, -5.0, 6.1, 0.0};
 
  double x(0.5);
 
  std::cout << "<- xd                                      = " << xd << '\n';
  std::cout << "<- n                                       = " << n << '\n';
  std::cout << "<- l                                       = " << l << '\n';
  std::cout << "<- x                                       = " << x << '\n';
 
  std::cout << "-> gegenbauer(n, l, xd)                      = " << kyosu::gegenbauer(n, l, xd) << '\n';
  std::cout << " ====================================================== " << std::endl;
  std::cout << "-> gegenbauer[eve::ignore_last(2)](n, l, xd) = " << kyosu::gegenbauer[eve::ignore_last(2)](n, l, xd)
            << '\n';
  std::cout << "-> gegenbauer[n > 3](n, l, xd)               = " << kyosu::gegenbauer[n > 3](n, l, xd) << '\n';
  std::cout << "-> gegenbauer(3.0, 2.0, xd)                  = " << kyosu::gegenbauer(3.0, 2.0, xd) << '\n';
  std::cout << "-> gegenbauer(n, l, 2.0)                     = " << kyosu::gegenbauer(n, l, 2.0) << '\n';
  std::cout << "-> gegenbauer(n, l, x)                       = " << kyosu::gegenbauer(n, l, x) << '\n';
}