Meijer G-function at the origin

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SUMMARY

The discussion centers on the evaluation of the Meijer G-function, specifically G7,00,7(x | 1, 7/6, 4/3, 4/3, 3/2, 5/3, 11/6, 0, 5/6, 7/6, 4/3, 3/2, 5/3, 11/6) at the point x=0. Users express frustration with Mathematica's inability to compute this function at the origin, with one participant suggesting that the function vanishes at this point. However, another contributor clarifies that the function is not defined at x=0, as both the numerator and denominator approach ±∞, indicating that a definitive evaluation is not possible.

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muppet
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Hi all,
I asked Mathematica to evaluate a Meijer-G function for me, and it point blank refuses to. (See a related post in the Math and Science Software subforum...)
I was wondering if anyone here could tell me anything about the behaviour of the function
[tex]G^{7,0}_{0,7}\left( x\bigg | \stackrel{}{1}\stackrel{\ }{\frac{7}{6}}\stackrel{\ }{\frac{4}{3}}\stackrel{\ }{\frac{4}{3}}\stackrel{}{\frac{3}{2}} \stackrel{}{\frac{5}{3}}\stackrel{}{\frac{11}{6}} \stackrel{}{0} \stackrel{}{\frac{5}{6}} \stackrel{}{\frac{7}{6}}\stackrel{}{\frac{4}{3}} \stackrel{}{\frac{3}{2}} \stackrel{}{\frac{5}{3}} \stackrel{}{\frac{11}{6}} \right)[/tex]
at the point [itex]x=0[/itex].
(apologies for my inability to Latex; in the proper conventional notation, all of these numbers would be on the bottom row, with the row at the top blank, as I hope is clear from the index structure).

I'm under the impression that this vanishes, but that's based on information I've extracted from Mathematica, which clearly isn't my friend at the moment. Does anyone know a different way in which I could check this?

Thanks in advance.
 
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As it cannot defined for ##x=0## and numerator as well as denominator tend to ##\pm \infty##, we can't expect any serious answer to your question.
 

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