R: Recurrence relations for ultraspherical polynomials
ultraspherical.recurrences
R Documentation
Recurrence relations for ultraspherical polynomials
Description
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 ultraspherical polynomial, C_k^{≤ft( α
ight)} ≤ft( x
ight),
and for orders k = 0,;1,; … ,;n.
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
ultraspherical.recurrences
Examples
###
### generate the recurrence relations for
### the normalized ultraspherical polynomials
### of orders 0 to 10
### polynomial parameter value is 1.0
###
normalized.r <- ultraspherical.recurrences( 10, 1, normalized=TRUE )
print( normalized.r )
###
### generate the recurrence relations for
### the normalized ultraspherical polynomials
### of orders 0 to 10
### polynomial parameter value is 1.0
###
unnormalized.r <- ultraspherical.recurrences( 10, 1, normalized=FALSE )
print( unnormalized.r )