Bug in analytical sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg100244] Bug in analytical sum*From*: Sebastian Meznaric <meznaric at gmail.com>*Date*: Fri, 29 May 2009 20:57:06 -0400 (EDT)

Consider the following sum f[k_] := Sum[n! (-I \[Alpha])^n Cos[\[Phi]/2]^n \[Alpha]^n Sin[\[Phi]/ 2]^n, {n, 0, k}]/Sum[n! \[Alpha]^(2 n) Cos[\[Phi]/2]^(2 n), {n, 0, k}] I am interested in taking alpha and k to infinity. Now clearly for finite k this is just a rational function in alpha. So if we want to take alpha to infinity we should get (-i Tan[\[Phi]/2])^k. But try this in Mathematica Limit[f[k], \[Alpha] -> \[Infinity]] and you will get I Cot[\[Phi]/2]. This is Mathematica 7.0.0. The reason seems to be that Mathematica evaluates the sum first and obtains a fraction consisting of the incomplete gamma functions and Ei integrals. It seems that the limits of those functions are not taken properly.

**Follow-Ups**:**Re: Bug in analytical sum***From:*danl@wolfram.com