Re: -- An exact simplification challenge - 55 (MeijerG) - Proud Earthling, go and prove our lifemanship over all the small-minded CASs!

On Mar 24, 1:47 pm, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
Hello computer algebra Fan the Earthling,

Training hard? Daily? Attaboy! Consider, constant training is
our human's terrific armo.

The Ultimate Action (for freedom, nuts and beer) is near!

Nail, once and for all, our human's carbon-based mind's absolute
supremacy over the wicked silicon (striped!) Computers coming!

Each morning, drill... until it's not too late... so....

Is there a Lion-Hearted Human Warrior the Simplifier to excogitate
a slim nice string of CAS commands to "elementarize" these

MeijerG[{{1/4, 1/2, 3/4}, {}}, {{0, 1/2, 1/2}, {}}, 1]

In[187]:=
2 2^(1/4) \[Pi]^(
3/2) ((\[Pi] - ArcTan[Sqrt[2 (1 + Sqrt[2])]]) Cos[\[Pi]/8] -
ArcTanh[Sqrt[2 (-1 + Sqrt[2])]] Sin[\[Pi]/8]) -
MeijerG[{{1/4, 1/2, 3/4}, {}}, {{0, 1/2, 1/2}, {}}, 1`20]

Out[187]= 0.*10^-19 + 0.*10^-19 I


MeijerG[{{1/6,1/6,1/2,2/3,5/6},{}}, {{0,1/6,1/3,2/3,2/3},{}}, 1]

In[110]:= {(8 \[Pi]^(7/2) (\[Pi] - Sqrt[2] ArcCoth[Sqrt[2]]))/Sqrt[
3], (4 \[Pi]^(7/2) (2 \[Pi] + Sqrt[2] Log[3 - 2 Sqrt[2]]))/Sqrt[
3]} - MeijerG[{{1/6, 1/6, 1/2, 2/3, 5/6}, {}}, {{0, 1/6, 1/3, 2/3,
2/3}, {}}, 1`20]

Out[110]= {0.*10^-18, 0.*10^-18}

The derivation of these is simple. Produce slater form of give
MeijerG,
collect factors and apply multiple arguments formula for Gamma in
reverse.
Then represent the corresponding Barnes integrals with convolution
equivalents,
which are elementary and feed it into Mathematica to get answers.
Massage to
get the nicer looking answers.

It might be pretty difficult to write a fully automated simplifier
which
can do this simplification automatically.

Oleksandr


?
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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