| 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^{\left( {\alpha ,\beta } \right)} \left( x \right),
and for orders k = 0,\;1,\; \ldots ,\;n.
Usage
jacobi.p.recurrences(n, alpha, beta, normalized=FALSE)
Arguments
n |
integer value for the highest polynomial order |
alpha |
numeric value for the first polynomial parameter |
beta |
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 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.
Szego, G., 1939. Orthogonal Polynomials, 23, American Mathematical Society Colloquium Publications, Providence, RI.
See Also
jacobi.p.inner.products,
pochhammer
Examples
###
### generate the recurrences data frame for
### the normalized Jacobi P polynomials
### of orders 0 to 10.
### parameter a is 2 and parameter b is 2
###
normalized.r <- jacobi.p.recurrences( 10, 2, 2, normalized=TRUE )
print( normalized.r )
###
### generate the recurrences data frame for
### the unnormalized Jacobi P polynomials
### of orders 0 to 10.
### parameter a is 2 and parameter b is 2
###
unnormalized.r <- jacobi.p.recurrences( 10, 2, 2, normalized=FALSE )
print( unnormalized.r )