| slegendre.polynomials {orthopolynom} | R Documentation |
Create list of shifted Legendre polynomials
Description
This function returns a list with n + 1 elements containing
the order k shifted Legendre polynomials, P_k^* \left( x \right),
for orders k = 0,\;1,\; \ldots ,\;n.
Usage
slegendre.polynomials(n, normalized=FALSE)
Arguments
n |
integer value for the highest polynomial order |
normalized |
a boolean value which, if TRUE, returns a list of normalized orthogonal polynomials |
Details
The function slegendre.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 shifted Legendre polynomial |
2 |
order 1 shifted Legendre 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
slegendre.recurrences,
orthogonal.polynomials,
orthonormal.polynomials
Examples
###
### gemerate a list of normalized shifted Legendre polynomials of orders 0 to 10
###
normalized.p.list <- slegendre.polynomials( 10, normalized=TRUE )
print( normalized.p.list )
###
### gemerate a list of unnormalized shifted Legendre polynomials of orders 0 to 10
###
unnormalized.p.list <- slegendre.polynomials( 10, normalized=FALSE )
print( unnormalized.p.list )