bug in Legendre polinomials
- To: mathgroup at smc.vnet.net
- Subject: [mg20346] bug in Legendre polinomials
- From: Peter Pollner <pollner at physik.uni-marburg.de>
- Date: Sat, 16 Oct 1999 00:47:38 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
I have found a misterious bug (Version 4.0.1.0):
I have checked the identity:
Sum[Binomial[ktmp, i]^2 x^i, {i, 0, ktmp}] = (1 - x)^ktmp LegendreP[ktmp,
(x + 1)/(1 - x)]
using:
Simplify[Sum[
Binomial[ktmp, i]^2 x^i, {i, 0, ktmp}] - (1 - x)^ktmp LegendreP[
ktmp, (x + 1)/(1 - x)]]
which should be zero for arbitrary ktmp integers.
Mathematica gives only for ktmp<36 the correct result
for ktmp>=36 it gives a nonvanishing polinom.
I am interested also to force Mathematica to give the result of the series
Sum[Binomial[ktmp, i]^2 x^i, {i, 0, ktmp}]
in terms of Legendre polinomials and not as terms of Hypergeometric
functions.
Thanks
Peter