legendre.recurrences: Recurrence relations for Legendre polynomials

In orthopolynom: Collection of Functions for Orthogonal and Orthonormal Polynomials

Recurrence relations for Legendre 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 Legendre polynomial, P_k ≤ft( x \right), and for orders k = 0,\;1,\; … ,\;n.

Usage

legendre.recurrences(n, normalized=FALSE)

Arguments

n	integer value for the highest polynomial order
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

legendre.inner.products

Examples

###
### generate the recurrences data frame for 
### the normalized Legendre polynomials
### of orders 0 to 10.
###
normalized.r <- legendre.recurrences( 10, normalized=TRUE )
print( normalized.r )
###
### generate the recurrences data frame for 
### the normalized Legendre polynomials
### of orders 0 to 10.
###
unnormalized.r <- legendre.recurrences( 10, normalized=FALSE )
print( unnormalized.r )

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