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Question: how to evaluate double infinite sum very quickly

Question:how to evaluate double infinite sum very quickly

shimaa sadk 45 Maple
integration sum numeric summation
July 24 2018
1

i have a prablem i work on it consiste of  aloop of 1000 iteration ,  and  apart of it evaluate the following sum  and integration  but maple either take very long time  about (12 hours) in evaluating it  (and it's very long )

 

or it get stuck . Is there any way to make maple evaluate this sum and integration  very quickely and didnt get stuck 


 

NULL

> 

`λλ`[1] := .1111111; `λλ`[2] := 2222222; `αα` := 1.51222222
> 

P := simplify(sum(sum((t+1)*`αα`^2*(1-`αα`)^(t+T)/(t+1+`λλ`[1]*(T+1)/`λλ`[2]), t = 0 .. infinity), T = 0 .. infinity))

Warning,  computation interrupted

  
> 

r[1] := exp(-C*(int(lambda[1]*alpha^2*exp(lambda[1]*Z)/((exp(lambda[1]*Z)-1+alpha)^2*(exp(lambda[2]*Z)-1+alpha)), Z = 0 .. infinity, numeric)));

exp(-C*(int(lambda[1]*alpha^2*exp(lambda[1]*Z)/((exp(lambda[1]*Z)-1.+alpha)^2*(exp(lambda[2]*Z)-1.+alpha)), Z = 0. .. Float(infinity))))

 (1)
> 

``
> 

R[1] := diff(r[1], lambda[1]):

 

> 

lambda[1] := 1.117480:
> 

``
> 

C := -2:
> 

r_r[1] := evalf(r[1]);

6.833764322

  

.5388679374

  

-1.033616758

  

4.934912438

  

-0.3143256678e-1

  

-4.822756149

  

4.934912438

  

-5.541440349

  

.2813149492

  

0.4011667571e-1

  

-0.3143256678e-1

  

.2813149492

  

-0.7207815680e-2

 (2)
> 

NULL


 

D

 
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