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Topic: Ask for help to evaluate an equation
Replies: 3   Last Post: Dec 16, 2012 3:51 PM

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Nasser Abbasi

Posts: 5,600
Registered: 2/7/05
Re: Ask for help to evaluate an equation
Posted: Dec 15, 2012 1:10 PM
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On 12/15/2012 11:29 AM, hpe650820@gmail.com wrote:
> I want to evaluate the following equation with mathematica but it seems i'm doing something wrong.
>
> Sum[(-1)^n/A^(n+1)t^(1+n-k(1-eta))beta^(n-k) Binomial[n,k](alpha Gamma[1-eta])^k/Gamma[2+n-k(1-eta)],{n,0,Infinity},{k,0,Infinity}]
>
> Any help would be appreciate it
>
> Hugo Perea
>


The sum over K can't be handled. But the sum over n does result in
closed form:

-----------------------------
s = (-1)^n/A^(n + 1) t^(1 + n - k (1 - eta)) beta^(n - k) Binomial[n,
k] (alpha Gamma[1 - eta])^k/Gamma[2 + n - k (1 - eta)]

r = Sum[s, {n, 0, Infinity}]
--------------------------------------------

(t^(1 - (1 - eta)*k)*Binomial[0, k]*(alpha*Gamma[1 - eta])^k*HypergeometricPFQ[{1, 1},
{1 - k, 2 - k + eta*k}, -((beta*t)/A)])/(beta^k*(A*Gamma[2 - k + eta*k]))

now

r = Sum[r, {k, 0, Infinity}]

does nothing. returns unevaluated.

Version 9

--Nasser
ps. good idea not to use UpperCase for symbols. Might conflict with
Mathematica's own.



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