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