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Question: The result does not seem to terminate.

Question:The result does not seem to terminate.

q41b3 20 Maple
sum binomial
June 27 2019
0


 

> 

restart
> 

with(Statistics)
> 

seq(sum((binomial(2*k, k)/4^k)^d, k = 1 .. infinity), d = [3, 4, 5, 6])

MeijerG([[1], [2, 2, 2]], [[3/2, 3/2, 3/2, 1], []], -1)/Pi^(3/2), MeijerG([[1], [2, 2, 2, 2]], [[3/2, 3/2, 3/2, 3/2, 1], []], -1)/Pi^2, MeijerG([[1], [2, 2, 2, 2, 2]], [[3/2, 3/2, 3/2, 3/2, 3/2, 1], []], -1)/Pi^(5/2), MeijerG([[1], [2, 2, 2, 2, 2, 2]], [[3/2, 3/2, 3/2, 3/2, 3/2, 3/2, 1], []], -1)/Pi^3

 (1)
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Download sum(binomial_with_higer_dim).mw

 The result does not seem to terminate whem I use evalf([%]).  The result should be like this:

(1/8)hypergeom([1,3/2,3/2,3/2],[2,2,2],1), (1/16)hypergeom([1,3/2,3/2,3/2,3/2],[2,2,2,2],1),(1/32)hypergeom([1,3/2,3/2,3/2,3/2,3/2],[2,2,2,2,2],1), (1/64)hypergeom([1,3/2,3/2,3/2,3/2,3/2,3/2],[2,2,2,2,2,2],1)

Thanks in advance.

 

 
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