Meijer G-function at the origin

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In summary, the speaker asked for information about the behavior of a Meijer-G function and its evaluation at x=0. They were unable to get an answer from Mathematica and were wondering if anyone else could provide insight. Another participant pointed out that the function cannot be defined for x=0 and therefore cannot be evaluated.
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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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  • #2
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.
 

Related to Meijer G-function at the origin

What is the Meijer G-function at the origin?

The Meijer G-function at the origin is a special mathematical function that is defined as the integral of a product of two or more functions. It is named after the mathematician Cornelis Meijer and is denoted by G(z).

What is the significance of the Meijer G-function at the origin?

The Meijer G-function at the origin has many applications in mathematics, engineering, and physics. It is used to solve various types of differential equations, evaluate complex integrals, and model physical phenomena.

How is the Meijer G-function at the origin different from other special functions?

The Meijer G-function at the origin has several unique properties that distinguish it from other special functions. It is a generalization of many other special functions, and it can be expressed as a combination of familiar functions such as exponential, trigonometric, and logarithmic functions.

What are the conditions for the convergence of the Meijer G-function at the origin?

The Meijer G-function at the origin has a complex domain of convergence, and its convergence depends on the values of its parameters. For certain parameter values, the function may converge for all complex numbers, while for others, it may have a restricted domain of convergence.

How is the Meijer G-function at the origin calculated?

The Meijer G-function at the origin can be calculated using various techniques, such as contour integration and series expansions. In some cases, it can also be expressed in terms of other well-known special functions, making its calculation simpler. Additionally, there are computer algorithms and software packages available for computing the Meijer G-function at the origin.

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