| slegendre.recurrences {orthopolynom} | R Documentation |
Recurrence relations for shifted 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 shifted Legendre polynomial, P_k^* \left( x \right), and
for orders k = 0,\;1,\; \ldots ,\;n.
Usage
slegendre.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 fnovomes@poly.edu
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.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992. Numerical Recipes in C, Cambridge University Press, Cambridge, U.K.
Szego, G., 1939. Orthogonal Polynomials, 23, American Mathematical Society Colloquium Publications, Providence, RI.
See Also
Examples
###
### generate the recurrence relations for normalized shifted Legendre polynomials
### of orders 0 to 10
###
normalized.r <- slegendre.recurrences( 10, normalized=TRUE )
print( normalized.r )
###
### generate the recurrence relations for normalized shifted Legendre polynomials
### of orders 0 to 10
###
unnormalized.r <- slegendre.recurrences( 10, normalized=FALSE )
print( unnormalized.r )