Loading [MathJax]/extensions/tex2jax.js
kyosu v0.1.0
Complex Without Complexes
 
•All Classes Namespaces Functions Variables Typedefs Modules Pages Concepts
Loading...
Searching...
No Matches

◆ tchebytchev

kyosu::tchebytchev = eve::functor<tchebytchev_t>
inlineconstexpr

Computes the value of the Tchebytchev polynomial of order n at z:

  • The Tchebytchev polynomial of order n is given by \( \displaystyle \mbox{T}_{n}(x) = \cos(n\arccos(x))\)

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace eve
{
// Regular overload
auto constexpr tchebytchev(kyosu::concepts::real auto n, kyosu::concepts::cayley_dickson auto z) noexcept; // 1
auto constexpr tchebytchev(kyosu::concepts::real auto n, kyosu::concepts::real auto z) noexcept; // 1
// Lanes masking
constexpr auto tchebytchev[conditional_expr auto c](/* any previous overload */) noexcept; // 2
constexpr auto tchebytchev[logical_value auto m](/* any previous overload */) noexcept; // 2
// Semantic options
constexpr auto tchebytchev[kind_1](/* any previous overload */) noexcept; // 1
constexpr auto tchebytchev[kind_2](i/* any previous overload */) noexcept; // 3
constexpr auto tchebytchev[successor]( kyosu::concepts::cayley_dickson auto z,
kyosu::cayley_dickson auto tn,
kyosu::cayley_dickson auto tnm1) noexcept; // 4
}
kyosu::concepts::cayley_dickson
General Cayley-dickson concept.
Definition: concepts.hpp:41
kyosu::concepts::real
General real concept.
Definition: concepts.hpp:48
kyosu::i
constexpr auto i
Computes the complex number in the chosen type.
Definition: i.hpp:69
kyosu::tchebytchev
constexpr auto tchebytchev
Computes the value of the Tchebytchev polynomial of order n at z:
Definition: tchebytchev.hpp:124
kyosu::cayley_dickson
Cayley-Dickson algebra main abstraction It is built so that all operation over C, Q and other such al...
Definition: cayley_dickson.hpp:32

Parameters

  • n : integral positive arguments. (note that negative values return a NaN)
  • x : real floating argument.

Return value

1.The value of the polynomial at z is returned.

  1. The operation is performed conditionnaly.
  2. evaluates the nth polynomial of tchebytchev of second kind \( \displaystyle U_n(z) = \frac{\sin(n\arccos z)}{\sin(\arccos z)}\).
  3. computes the value of \(T_{n+1}(z)\) knowing the values tn = \(T_n(z)\) and tnm1 = \(T_{n-1}(z)\), This call can be used to create a sequence of values evaluated at the same z and for rising n.

External references

Example