ultraspherical.recurrences {orthopolynom} | R Documentation |
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^{( α )} ( x ), and for orders $k$ = 0, 1, ... , $n$.
ultraspherical.recurrences(n, alpha, normalized=FALSE)
n |
integer highest polynomial order |
alpha |
polynomial parameter |
normalized |
boolean value which, if TRUE, returns recurrence relations for normalized polynomials |
A data frame with the recurrence relation parameters.
Frederick Novomestky fnovomes@poly.edu
Abramowitz and Stegun (1968)
normalized.r <- ultraspherical.recurrences( 10, 1, normalized=TRUE ) unnormalized.r <- ultraspherical.recurrences( 10, 1, normalized=FALSE )