Re: An exact simplification challenge - 49 (MeijerG) - go and surpass all the CASs!

On Jan 29, 3:22 pm, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
Hello computer algebra buffs,

Your guesswork is right, again! All the modern computer algebra
systems fail to simplify this directly...

Is there a Brave Human Simplifier to come up with the steps to
"elementarize" (and squeeze much!) this specfunction nightmare

+ MeijerG([[1], [5/4, 3/2]], [[3/4, 3/4, 1/4], []], -1)
- MeijerG([[1], [1/2, 3/4]], [[1/4, 1/4, -1/4], []], -1)

?

answer = 8*Sqrt[2]*Pi;

The proof goes by turning MeijerGs into sum over left poles and
combining
these sums. Thus gives

4 Sqrt[2] Pi + Sum[((2^(3/2 - 2*k)*Gamma[1/2 + 2*k])/((1 +
2*k)*Sqrt[Pi]*
Gamma[1 + k]^2))*(4*Log[4] + 3*PolyGamma[0, 1 + k] +
PolyGamma[0, 3/2 + k] - 4*PolyGamma[0, 1 + 4*k]), {k, 0,
Infinity}]

The sum, turns out to be 4 Sqrt[2] Pi itself, hence the answer. I do
realize this is
not a proof, rather a hint.


Oleksandr Pavlyk
Best wishes,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLChttp://maple.bug-list.org/ Maple Bugs Encyclopaediahttp://www.CAS-testing.org/ CAS Testing

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