Re: Infinite Series Error - Bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg124567] Re: Infinite Series Error - Bug?*From*: Devendra Kapadia <dkapadia at wolfram.com>*Date*: Wed, 25 Jan 2012 07:02:29 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hello Jimmy, Thank you for reporting the error with the infinite sum considered by you. The unexpected Power::infy messages are given due to a problem with the singularity test for this class of infinite sums. A possible workaround for the issue is to compute the corresponding finite sum and then use Limit to obtain the required value for the infinite sum, as shown below. ====================== In[2]:= Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, m}] /. {q -> 0.1} Out[2]= -21.1013 + 1.08574 QPolyGamma[0, -0.25 + m, 0.0001] In[3]:= Limit[%, m -> Infinity] Out[3]= -21.1012 In[4]:= Block[{q = 0.1}, NSum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, Infinity}]] Out[4]= -21.1012 ====================== I apologize for the inconvenience caused by this problem. Sincerely, Devendra Kapadia, Wolfram Research, Inc. ----- Original Message ----- From: "clashton" <clashton at gmail.com> To: mathgroup at smc.vnet.net Sent: Tuesday, January 24, 2012 4:06:02 AM Subject: [mg124567] Infinite Series Error - Bug? 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