       Re: MMA3.0.0 bug in symbolic summation

• To: mathgroup at smc.vnet.net
• Subject: [mg9063] Re: [mg8969] MMA3.0.0 bug in symbolic summation
• From: Olivier Gerard <jacquesg at pratique.fr>
• Date: Thu, 9 Oct 1997 01:42:43 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```At 07:59 +0200 97.10.06, luca ciotti wrote:
> Dear Users,
>
> I found a problem in symbolic summation using MMA 3.0.0.
>
>  A = Sum[ Exp[-k]/(1+k^3), {k,0,Infinity}]
>
> The analitycal result, when evaluated numerically  is
>
>                           N[A,50] = 0.5344386.....
>
>
> This is obviously wrong, in fact each term of the series is
> positive, and the first (k=0) is equal 1.
>
> Performing directly NSum, return 1.20111.....
>
>
> Is this bug still present in MMA3.0.1?
>
Dear Luca,

I tested this sum on a 3.0.1 version on a PowerMacintosh and got
the same answer. Doing a few experiments, the same sum but with
(a+k^2) gives a correct answer and (1+k^4) causes too nested
computations (\$RecursionLimit::reclim   Error message) but as
the possibilities for even exponents are not the same as for
odd ones, this not very probant.

As the first step of the standard procedure for this kind of sums
is to transform the 1/(1+k^3) fraction into a sum of fractions of the kind
1/(a+k)^r where a and r are fixed, I did myself a few transforms
and let Mma do the final steps (transformations into Hypergeometric,
LerchPhi, PolyGamma functions)  and I got the same incorrect real part
with varying imaginary parts.

So the bug, if this one seems to be in the use of Special Functions
to express the sum.

Making experiments with the simpler
Sum[ 1/(1+k^g) , {k,0, Infinity}]

I have correct results for k=2,3,4 but have a

Union::normal : Nonatomic expression expected at position 1 in Union[False]

Error Message for k=5, 6, ... (although the symbolic result given is
evaluatable to the correct value with a near-zero imaginary part)

I find all that really annoying.

Olivier

```

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