So, for anyone interested, I was able to *sort-of* solve the Gegenbauer polynomial problem.
Using a lambda-function: C = lambda (n, Lambda, x): sum( [(2*x)^(n-2*m)*(-1)^(m)*rising_factorial(Lambda,n-m)/(factorial(m)*factorial(n-2*m)) for m in [0..floor(n/2)]] ) (the definition is taken from Higher Transcendental Functions, volume 2, page 175) You get that C([n,a,x]) yields polynomials which are equivalent to GegenbauerC[n,a,x] in Mathematica (see here<http://mathworld.wolfram.com/GegenbauerPolynomial.html>) or GegenbauerC(n,a,x) in Maple (see here<http://www.maplesoft.com/support/help/Maple/view.aspx?path=GegenbauerC> ). The important thing to note about C([n,a,x]) is that C([2,-1/2,x]) doesn't throw up an error, where as ultraspherical(2,-1/2,x) does. Specifically, you get the error: TypeError: error evaluating "ultraspherical(2,-1/2,x)": Error executing code in Maxima CODE: ultraspherical(2,-1/2,x); Maxima ERROR: Division by 0 -- an error. To debug this try: debugmode(true); Since I know, personally, that there exists a Gegenbauer polynomial associated to n=2 and a=-1/2, this is extremely fishy (and annoying). I hope this code helps anyone trying to do any work in Sage with the ultraspherical(n,a,x) function. -Steven -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
