This function returns a vector with n + 1 elements containing the inner product of
an order k Chebyshev polynomial of the first kind, C_k ≤ft( x
ight),
with itself (i.e. the norm squared) for orders k = 0,;1,; … ,;n .
Usage
chebyshev.c.inner.products(n)
Arguments
n
integer value for the highest polynomial order
Details
The formula used to compute the inner products is as follows.
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
gegenbauer.inner.products
Examples
###
### generate the inner products vector for the
### C Chebyshev polynomials of orders 0 to 10
###
h <- chebyshev.c.inner.products( 10 )
print( h )