| jacobi.g.polynomials {orthopolynom} | R Documentation |
Create list of Jacobi polynomials
Description
This function returns a list with n + 1 elements containing
the order k Jacobi polynomials, G_k \left( {p,q,x} \right),
for orders k = 0,\;1,\; \ldots ,\;n.
Usage
jacobi.g.polynomials(n, p, q, normalized=FALSE)
Arguments
n |
integer value for the highest polynomial order |
p |
numeic value for the first polynomial parameter |
q |
numeric value for the second polynomial parameter |
normalized |
a boolean value which, if TRUE, returns a list of normalized orthogonal polynomials |
Details
The function jacobi.g.recurrences produces a data frame with the recurrence relation parameters
for the polynomials. If the normalized argument is FALSE, the
function orthogonal.polynomials is used to construct the list of orthogonal polynomial objects.
Otherwise, the function orthonormal.polynomials is used to construct the
list of orthonormal polynomial objects.
Value
A list of n + 1 polynomial objects
1 |
order 0 Jacobi polynomial |
2 |
order 1 Jacobi polynomial |
...
n+1 |
order |
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.g.recurrences,
orthogonal.polynomials,
orthonormal.polynomials
Examples
###
### gemerate a list of normalized Jacobi G polynomials of orders 0 to 10
### first parameter value p is 3 and second parameter value q is 2
###
normalized.p.list <- jacobi.g.polynomials( 10, 3, 2, normalized=TRUE )
print( normalized.p.list )
###
### gemerate a list of normalized Jacobi G polynomials of orders 0 to 10
### first parameter value p is 3 and second parameter value q is 2
###
unnormalized.p.list <- jacobi.g.polynomials( 10, 3, 2, normalized=FALSE )
print( unnormalized.p.list )