       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.
>