schebyshev.t.polynomials {orthopolynom}R Documentation

Create list of shifted Chebyshev polynomials

Description

This function returns a list with $n$+1 elements containing the order $k$ shifted Chebyshev polynomials of the first kind, T_k^* ( x), for orders $k$ = 0, 1, ..., $n$.

Usage

schebyshev.t.polynomials(n, normalized)

Arguments

n integer highest polynomial order
normalized a boolean value which, if TRUE, returns a list of normalized orthogonal polynomials

Details

The function produces a data frame with the recurrence relation parameters for the orthogonal polynomials. It then uses the function orthogonal.polynomials to construct the list of polynomial objects from the recurrence relations.

Value

A list of $n$+1 polynomial objects

1 order 0 shifted Chebyshev polynomial
2 order 1 shifted Chebyshev polynomial
n+1 order $n$ shifted Chebyshev polynomial

Author(s)

Frederick Novomestky fnovomes@poly.edu

References

Abramowitz and Stegun (1968)

See Also

schebyshev.u.recurrences, orthogonal.polynomials, orthonormal.polynomials

Examples

normalized.p.list <- schebyshev.t.polynomials( 10, normalized=TRUE )
unnormalized.p.list <- schebyshev.t.polynomials( 10, normalized=FALSE )

[Package orthopolynom version 1.0-1 Index]