This function returns a vector with n + 1 elements containing the inner product of
an order k ultraspherical polynomial, C_k^{≤ft( α
ight)} ≤ft( x
ight),
with itself (i.e. the norm squared) for orders k = 0,;1,; … ,;n .
Usage
ultraspherical.inner.products(n,alpha)
Arguments
n
integer value for the highest polynomial order
alpha
numeric value for the polynomial parameter
Details
This function uses the same formula as the function gegenbauer.inner.products.
Abramowitz, M. and I. A. Stegun, 1968. Handbook of Mathematical Functions with
Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., NY.
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
gegenbauer.inner.products
Examples
###
### generate the inner products vector for the
### ultraspherical polynomials of orders 0 to 10.
### the polynomial parameter is 1.0
###
h <- ultraspherical.inner.products( 10, 1 )
print( h )