This function returns a list with n + 1 elements containing
the order k ultraspherical polynomials, C_k^{≤ft( α
ight)} ≤ft( x
ight),
for orders k = 0,;1,; … ,;n.
a boolean value which, if TRUE, returns a list of normalized orthogonal polynomials
Details
The function ultraspherical.recurrences produces a data frame with the recurrence relation parameters
for the polynomials. If the normalized argument is FALSE, the
function orthogonal.polynomials is used to construct the list of orthogonal polynomial objects.
Otherwise, the function orthonormal.polynomials is used to construct the
list of orthonormal polynomial objects.
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.