Re: MeijerG



A collegue of mine came across this function during the course of the
inversion of one Fourier Transform.

He suceeded in writing this function it terms of the sum of two
products; each of these products
was consist of BesselK*StruveL. He didn't give me more details. He put
me as a chalenge if I could
use a CAS in order to arrive at his formula (he checked his formula
numerically). I didn't
manage to find anything also, that's why the presence of this thread!

As regards your statement about the analyticity of this function, with
all of my respect to your
knowledge, are you 100% sure?

I don't know how you came to this conclusion. Mathematica can't get
neither the limit as o->0,
nor at infinity. But look the following plot (I know that plot can be
misleading sometimes, but I think here
is not the case)...

In[10]:=
f[o_, m_] := MeijerG[{{1}, {}}, {{-2^(-1), 1/2}, {0}}, o^2/(4*m^2)]

In[14]:=
(Limit[f[o, 1], o -> #1] & ) /@ {0, Infinity}

Out[14]=
{Limit[MeijerG[{{1}, {}}, {{-(1/2), 1/2}, {0}}, o^2/4], o -> 0],
Limit[MeijerG[{{1}, {}}, {{-(1/2), 1/2}, {0}}, o^2/4],
o -> Infinity]}

In[21]:=
Plot[{f[x, 1], -x^(-1) - 2*Pi}, {x, 0, 10}, Axes -> False, Frame ->
{True, True, False, False}]

I think that the function behaves as -1/x at zero and as -2*Pi.

Dimitris



Ο/Η Bhuvanesh έγραψε:
I don't think it can be written in closed form in terms of anything else that is currently implemented in Mathematica/Maple. It's an entire function, though. How did you come across it?

Bhuvanesh,
Wolfram Research

.



Relevant Pages

  • Re: MeijerG
    ... He suceeded in writing this function it terms of the sum of two ... nor at infinity. ... But look the following plot (I know that plot can be ...
    (sci.math.symbolic)
  • Re: word limits and revision
    ... removing two-thirds of the reason for reading (or writing). ... considered slimming down the plot. ... much damage; do an experimental draft with it gone; and repeat until ... strongly, the Faerie King yarn, which has been knocking around for ten ...
    (rec.arts.sf.composition)
  • Re: Getting out of this world?
    ... writing), where you make assumptions that don't apply. ... (My backbrain is quite good at making up internally ... Magic Earth is an earth like ours, ... I don't doubt that someone could claim to find 'plot' in my stuff ...
    (rec.arts.sf.science)
  • Re: mode for a scene?
    ... writing, based on the outline. ... I do a little plot summary, ... to let the characters invent a new plot, ... I'm someone who can't even remember what all these Bickham terms mean. ...
    (rec.arts.sf.composition)
  • Re: Effects of Magic
    ... For me writing the real and the made up are not that different. ... necessary consequences in terms of plot, ... boy with silver hair wearing a sanctuary band and wonder why and then ... Daea, for instance, mixes and matches numbers of things that were never really contemporary in our world, There are reasons for that, and I think they stand, up to a point -- but really, a world where swords-and-sorcery on the one side and machine-guns-and-railroads on the other really do form a credible balance of power, almost certainly wouldn't look like that at all. ...
    (rec.arts.sf.composition)