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chebyshev
In mathematics the Chebyshev polynomials are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively. One usually distinguishes between Chebyshev polynomials of the first kind which are denoted Tn and Chebyshev polynomials of the second kind which are denoted Un. The letter T is used because of the alternative transliterations of the name Chebyshev as Tchebycheff (French) or Tschebyschow (German). This function corresponds to the Chebyshev polynomials of first kind.
Evaluates the Chebyshev polynomial of some order n at the given point x in R.
Argument n
Scalar
Argument x
Scalar
Returns 1. entry
Scalar
chebyshev(3, 0.5)
Evaluates the Chebyshev polynomial of order 3 at the point x = 0.5.
Evaluates the Chebyshev polynomial of some order n at the given points in the matrix X in R.
Argument n
Scalar
Argument X
Matrix
Returns 1. entry
Matrix
chebyshev(1, [-1, 0.5, 0, 0.5, 1])
Evaluates the first Chebyshev polynomial (which is just x), at the points -1 to 1 with a spacing of 0.5.