Groups > comp.soft-sys.math.maple > #337

Re: Series Summation Question

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From	Axel Vogt <&noreply@axelvogt.de>
Newsgroups	comp.soft-sys.math.maple
Subject	Re: Series Summation Question
Date	Sat, 28 Jan 2012 20:21:44 +0100
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On 27.01.2012 07:55, Peter Pein wrote:
...
>> Well, if you are interested in the approximation of the sum's value for
>> q=1/10, you should have used NSum in Mathematica:
>>
>> NSum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)) /. q->1/10, {n, 0, Infinity},
>> WorkingPrecision->20]
>>
>> -21.101200102001001100
>>
>> or - using your workaround - get
>>
>> 6/(5*(-1 + q)) + (1 + 2*q + 3*q^2 + 4*q^3)/(5*(1 + q + q^2 + q^3 + q^4))
>> + (-2*Log[q^4] + Log[1 - q^4] + QPolyGamma[0, 2 - Log[q^5]/Log[q^4],
>> q^4])/(q*Log[q^4])
>>
>> as (hopefully) exact value.
>>
>> Cheers, Peter
>
> Sorry for posting too fast. One gets the result in a more simple form by doing sth. more complicated:
>
> In[1]:= f[q_] = q^(-6 + 4*n)/(1 - q^(-5 + 4*n));
> assum = SumConvergence[f[q], n]
> s[q_] = Together[Subtract @@ (Limit[Sum[f[q], n], n -> #1, Assumptions -> assum] & ) /@ {Infinity, 0}]
> N[s[1/10]]
>
>
> Out[2]= q != 0 && Abs[q]^4 < 1
> Out[3]= (Log[1 - q^4] + QPolyGamma[0, -(Log[q^5]/Log[q^4]), q^4])/(q*Log[q^4])
> Out[4]= -21.1012

I am not aware that Maple has a command to find a
condition for convergence.

And it does not provide a symbolic solution (where
I guess the above cryptic command does just that)

Thread

Series Summation Question clashton <clashton@gmail.com> - 2012-01-25 22:46 -0800
  Re: Series Summation Question Axel Vogt <&noreply@axelvogt.de> - 2012-01-26 19:41 +0100
  Re: Series Summation Question Joe Riel <joer@san.rr.com> - 2012-01-26 08:21 -0800
    Re: Series Summation Question clashton <clashton@gmail.com> - 2012-01-26 16:45 -0800
      Re: Series Summation Question Peter Pein <petsie@dordos.net> - 2012-01-27 07:31 +0100
        Re: Series Summation Question Peter Pein <petsie@dordos.net> - 2012-01-27 07:55 +0100
          Re: Series Summation Question clashton <clashton@gmail.com> - 2012-01-28 07:59 -0800
          Re: Series Summation Question Axel Vogt <&noreply@axelvogt.de> - 2012-01-28 20:21 +0100
            Re: Series Summation Question Peter Pein <petsie@dordos.net> - 2012-02-02 12:21 +0100

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