Algorythms

Orthogonal Polynomials

Description: The OrthPol(KF, n, x) function computes orthogonal polynomials: Chebyshev, Laguerre, Hermite polynomials, and their derivatives using recurrence relations.

Parameters:

1. KF - parameter specifying the orthogonal polynomial
   • KF = 1 for Chebyshev polynomial of the first kind
   • KF = 2 for Chebyshev polynomial of the second kind
   • KF = 3 for Laguerre polynomial
   • KF = 4 for Hermite polynomial
2. n - integer order of orthogonal polynomial.
3. x - argument of orthogonal polynomial.

Return: Vector with values of the orthogonal polynomial (the first place) of order n with argument x, and its first derivatives (the second place).