Re: Infinite Series Error - Bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg124565] Re: Infinite Series Error - Bug?*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Wed, 25 Jan 2012 07:01:48 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201201241006.FAA20247@smc.vnet.net>

term = q^(-6 + 4*n)/(1 - q^(-5 + 4*n)); expr = Assuming[{Abs[q] < 1}, Sum[term, {n, 0, Infinity}]] (Log[1 - q^4] + QPolyGamma[0, -(Log[q^5]/Log[q^4]), q^4])/(q*Log[q^4]) expr /. q -> 0.1 -21.1012 Checking with a partial sum expr == Total[Table[term, {n, 0, 10}]] /. q -> 0.1 True The symbolic Sum also evaluates if the assumption is written as -1 < q < 1 expr == Assuming[{-1 < q < 1}, Sum[term, {n, 0, Infinity}]] True However, the problem arises if the assumption is restricted to positives Assuming[{0 < q < 1}, Sum[term, {n, 0, Infinity}]] Power::infy: Infinite expression 1/0 encountered. >> Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, Infinity}] Presumably the evaluation without an assumption goes down this path in some way. Bob Hanlon On Tue, Jan 24, 2012 at 5:06 AM, clashton <clashton at gmail.com> wrote: > Can anyone explain why evaluating the following expression gives an > error? > > Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, Infinity}] /. {q -> 0.1} > > None of the denominators are 0 (would only happen if -5 + 4*n=0, which > is impossible for an integer n, yet I get an error message "Infinite > expression 1/0 encountered" (several times in fact). > > Any help on a work around greatly appreciated. > > (Please reply to my personal e-mail also). > > Thanks, > > Jimmy >

**References**:**Infinite Series Error - Bug?***From:*clashton <clashton@gmail.com>