ultraspherical.polynomials {orthopolynom} | R Documentation |
This function returns a list with $n$+1 elements containing the order $k$ ultraspherical polynomials, C_k^{( α )} ( x ), for orders $k$ = 0, 1, ..., $n$.
ultraspherical.polynomials(n, alpha, normalized=FALSE)
n |
integer highest polynomial order |
alpha |
polynomial parameter |
normalized |
a boolean value which, if TRUE, returns a list of normalized orthogonal polynomials |
The function produces a data frame with the recurrence relation parameters for the orthogonal polynomials. It then uses the function orthogonal.polynomials
to construct the list of polynomial objects from the recurrence relations.
A list of $n$+1 polynomial objects
1 |
order 0 ultraspherical polynomial |
2 |
order 1 ultraspherical polynomial |
n+1 |
order $n$ ultraspherical polynomial |
Frederick Novomestky fnovomes@poly.edu
Abramowitz and Stegun (1968)
gegenbauer.recurrences
,
orthogonal.polynomials
,
orthonormal.polynomials
normalized.p.list <- ultraspherical.polynomials( 10, 1, normalized=TRUE ) unnormalized.p.list <- ultraspherical.polynomials( 10, 1, normalized=FALSE )