From: "Burcin Erocal" <[EMAIL PROTECTED]> > > it doesn't give an answer. This means that your expression doesn't have > a hypergeometric closed form in the sense of A=B, p. 143 [1]: > > http://www.cis.upenn.edu/~wilf/AeqB.html
Is this a joke? After converting binomial coefficients to Pochhammer symbols, it is exactly the definition of Hypergeometric1F1[-n,-2n,2x] for positive integer n, or 1 for n=0. > Sage will have symbolic summation capabilities soon, but I doubt if it > will ever be able to simplify this expression. I hope it will. Eric Weisstein wrote to me that the current development version of Mathematica gives the answer Hypergeometric1F1[-n,-2n,2x]. > What are your expectations from a "correct answer"? How did you come > across this example? If you know/conjecture a simpler form for this > expression, you can prove that they are equal by showing that they both > satisfy the above recurrence, and agree on the inital values. I came across this example in a recent thread in Maple newsgroup. The correct answer is 1 for n=0 and Hypergeometric1F1[-n, -2 n, 2 x] for integer n>0, which would be equal to the expression given by Mathematica if n was not a positive integer. Another form of the correct answer is (2 x)^(n+1/2) E^x BesselK[n+1/2,x] n!/(2 n)!/Sqrt[Pi] Alec --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
