jacobi.p.polynomials {orthopolynom}R Documentation

Create list of Jacobi polynomials

Description

This function returns a list with $n$+1 elements containing the order $k$ Jacobi polynomials, P_k^{( {α ,β } )} ( x ), for orders $k$ = 0, 1, ..., $n$.

Usage

jacobi.p.polynomials(n, a, b, normalized=FALSE)

Arguments

n integer highest polynomial order
a first polynomial parameter
b second polynomial parameter
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 Jacobi polynomial
2 order 1 Jacobi polynomial
n+1 order $n$ Chebyshev polynomial

Author(s)

Frederick Novomestky fnovomes@poly.edu

References

Abramowitz and Stegun (1968)

See Also

jacobi.p.recurrences, orthogonal.polynomials, orthonormal.polynomials

Examples

normalized.p.list <- jacobi.p.polynomials( 10, 2, 2, normalized=TRUE )
unnormalized.p.list <- jacobi.p.polynomials( 10, 2, 2, normalized=FALSE )

[Package orthopolynom version 1.0-1 Index]