> There is reason to believe that the two G in front should result in
> -1/4. At this point the algorithm seems to be incomplete ...

To justify this reason I should post this too:


In [75]: hyperexpand(G1, allow_hyper=True)
Out[75]: meijerg(((1,), (3,)), ((2,), (0,)), -1)

In [76]: hyperexpand(G2, allow_hyper=True)
Out[76]: 1/2

In [77]: hyperexpand(G3, allow_hyper=True)
Out[77]: meijerg(((3, 1), ()), ((), (2, 0)), -1)

In [78]: hyperexpand(G4, allow_hyper=True)
Out[78]: 0



In [79]: G1.evalf(n=50)
Out[79]: 0.50000000000000000000000000000000000000000000000000

In [80]: G2.evalf(n=50)
Out[80]: 0.50000000000000000000000000000000000000000000000000

In [81]: G3.evalf(n=50)
Out[81]: 0

In [82]: G4.evalf(n=50)
Out[82]: 0



In [83]: -G1/2 + G2/2 - G3/2 + G4/2
Out[83]: -meijerg(((1,), (3,)), ((2,), (0,)), -1)/2 + meijerg(((1,), (3,)), 
((2,), (0,)), 1)/2 - meijerg(((3, 1), ()), ((), (2, 0)), -1)/2 + meijerg(((3, 
1), ()), ((), (2, 0)), 1)/2

In [85]: _.evalf(n=50)
Out[85]: 0.e-160

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