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Re: Infinite Series Error - Bug?

  • To: mathgroup at
  • Subject: [mg124567] Re: Infinite Series Error - Bug?
  • From: Devendra Kapadia <dkapadia at>
  • Date: Wed, 25 Jan 2012 07:02:29 -0500 (EST)
  • Delivered-to:

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.


Devendra Kapadia,
Wolfram Research, Inc.

----- Original Message -----
From: "clashton" <clashton at>
To: mathgroup at
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

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).



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