jacobi.p.recurrences {orthopolynom}R Documentation

Recurrence relations for Jacobi polynomials

Description

This function returns a data frame with $n$+1 rows and four named columns containing the coefficient vectors c, d, e and f of the recurrence relations for the order $k$ Jacobi polynomial, P_k^{( {α ,β } )} ( x ), and for orders $k$ = 0, 1, ... , $n$.

Usage

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

Arguments

n integer highest polynomial order
a first polynomial parameter
b second polynomial parameter
normalized boolean value which, if TRUE, returns recurrence relations for normalized polynomials

Value

A data frame with the recurrence relation parameters.

Author(s)

Frederick Novomestky fnovomes@poly.edu

References

Abramowitz and Stegun (1968)

See Also

jacobi.p.inner.products, pochhammer

Examples

normalized.r <- jacobi.p.recurrences( 10, 2, 2, normalized=TRUE )
unnormalized.r <- jacobi.p.recurrences( 10, 2, 2, normalized=FALSE )

[Package orthopolynom version 1.0-1 Index]