jacobi.g.recurrences: Recurrence relations for Jacobi polynomials

In orthopolynom: Collection of Functions for Orthogonal and Orthonormal Polynomials

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, G_k ≤ft( {p,q,x} \right), and for orders k = 0,\;1,\; … ,\;n.

Usage

jacobi.g.recurrences(n, p, q, normalized=FALSE)

Arguments

n	integer value for the highest polynomial order
p	numeric value for the first polynomial parameter
q	numeric value for the 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 [e-mail]

References

Abramowitz, M. and I. A. Stegun, 1968. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York.

Courant, R., and D. Hilbert, 1989. Methods of Mathematical Physics, John Wiley, New York, NY.

Szego, G., 1939. Orthogonal Polynomials, 23, American Mathematical Society Colloquium Publications, Providence, RI.

See Also

jacobi.g.inner.products, pochhammer

Examples

###
### generate the recurrences data frame for 
### the normalized Jacobi G polynomials
### of orders 0 to 10.
### parameter p is 3 and parameter q is 2
###
normalized.r <- jacobi.g.recurrences( 10, 3, 2, normalized=TRUE )
print( normalized.r )
###
### generate the recurrences data frame for 
### the normalized Jacobi G polynomials
### of orders 0 to 10.
### parameter p is 3 and parameter q is 2
###
unnormalized.r <- jacobi.g.recurrences( 10, 3, 2, normalized=FALSE )
print( unnormalized.r )

orthopolynom documentation built on Oct. 3, 2022, 5:08 p.m.