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Error and confusing definition in ?MeijerG

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jfh

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May 15, 2012, 10:49:16 PM5/15/12
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In the definition of the MeijerG function, Maple 16 says

Contour L[gamma+infinity*I] starts at gamma-infinity and finishes at
gamma+infinity*I.

Other sources of information (Mathematica, Prudnikov et al.,
Gradshteyn & Ryzhik, Erdelyi) suggest that that contour starts at
gamma-infinity*I not gamma-infinity.

More confusingly, the notation defining m,n,p,q in the calling
sequence is not consistent with the m,n,p,q in the standard classical
notation. ?MeijerG says inter alia

Calling Sequence
MeijerG([as, bs], [cs, ds], z)
Parameters
as - list of the form [a1, ..., am]; first group of numerator GAMMA
parameters
bs - list of the form [b1, ..., bn]; first group of denominator GAMMA
parameters
cs - list of the form [c1, ..., cp]; second group of numerator GAMMA
parameters
ds - list of the form [d1, ..., dq]; second group of denominator
GAMMA
parameters
z - expression

o The classical notation used to represent the MeijerG function
relates to the
notation used in Maple by

"G[pq]^mn(z|( )[b[1], .., b[m],b[m+1], .., b[q]]^(a[1], .., a[n],a[n
+1], ..,
a[p]))=MeijerG([[a[1], .., a[n]],[a[n+1], .., a[p]]],[[b[1], .., b[m]],
[b[m+1],
.., b[q]]],z)"

The calling sequence definitions of m,n,p,q suggest that MeigerG([[],
[]],[[0],[],z) would be the classical Meijer G[10]^00(z) function but
of course it is really G[01]^10(z), which is exp(-x) according to
Prudnikov et al. vol. 3 p633 formula 8.4.3.1. Maple agrees, using its
own notation:

> convert(MeijerG([[],[]],[[0],[]],z),StandardFunctions);
exp(-z)

-- John Harper
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