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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
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