This function returns a data frame with n + 1 rows and four named columns containing
the coefficient vectors c, d, e and f of
the recurrence relations for the order k Chebyshev polynomial of the first kind, C_k ≤ft( x
ight),
and for orders k = 0,;1,; … ,;n.
Usage
chebyshev.c.recurrences(n, normalized=FALSE)
Arguments
n
integer value for the highest polynomial order
normalized
boolean value which, if TRUE, returns recurrence relations for normalized polynomials
Value
A data frame with the recurrence relation parameters.
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
chebyshev.c.inner.products
Examples
###
### generate the recurrences data frame for
### the normalized Chebyshev C polynomials
### of orders 0 to 10.
###
normalized.r <- chebyshev.c.recurrences( 10, normalized=TRUE )
print( normalized.r )
###
### generate the recurrences data frame for
### the normalized Chebyshev C polynomials
### of orders 0 to 10.
###
unnormalized.r <- chebyshev.c.recurrences( 10, normalized=FALSE )
print( unnormalized.r )