       Re: Infinite Series Error - Bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg124567] Re: Infinite Series Error - Bug?
• 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:= Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, m}] /. {q -> 0.1}

Out= -21.1013 + 1.08574 QPolyGamma[0, -0.25 + m, 0.0001]

In:= Limit[%, m -> Infinity]

Out= -21.1012

In:= Block[{q = 0.1},
NSum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, Infinity}]]

Out= -21.1012

======================

I apologize for the inconvenience caused by this problem.

Sincerely,

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.