| spherical.inner.products {orthopolynom} | R Documentation |
Inner products of spherical polynomials
Description
This function returns a vector with n + 1 elements containing the inner product
of an order k spherical polynomial, P_k \left( x \right),
with itself (i.e. the norm squared) for orders k = 0,\;1,\; \ldots ,\;n.
Usage
spherical.inner.products(n)
Arguments
n |
integer value for the highest polynomial order |
Details
The formula used to compute the inner products of the spherical orthogonal polynomials is the same as that used for the Legendre orthogonal polynomials.
Value
A vector with n + 1 elements
1 |
inner product of order 0 orthogonal polynomial |
2 |
inner product of order 1 orthogonal polynomial |
...
n+1 |
inner product of 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
Examples
###
### generate the inner products vector for the spherical polynomals
### of orders 0 to 10.
###
h <- spherical.inner.products( 10 )
print( h )