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Thank you in advance for your time and help. I am new with Fox H function. Allow me to ask some questions.

  1. why the definition is different between wiki and mathworld ? The links are below. You can see that the + and - sign are different in the gamma functions. wiki: https://en.wikipedia.org/wiki/Fox_H-function mathworld: http://mathworld.wolfram.com/FoxH-Function.html

  2. I do need to understand the meaning of the integration area, is there an example I can see? Thank you.

J. M. ain't a mathematician
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Sunson29
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  • Ad 1: Yes there is a sign change, but notice the same sign change in $z^s \rightarrow z^{-s},$ i.e. there is a substitution $s \rightarrow -s$ in the complete integrand. – gammatester Sep 28 '17 at 17:51
  • oh, thank you sir. May I ask what's the point or benefit to substitute s to -s ? and also where to see a detail example about the contour integration area for H function? Thank you again. – Sunson29 Sep 28 '17 at 22:17
  • It is a matter of convention. I think that $z^{-s}$ is preferable since it takes the form of an Inverse Mellin Transform. Scaling parameters positive reals is also a matter of convention. If they are negative reals, you can rewrite the Mellin Barnes integrand to make them positive. – Jorge Zuniga Mar 16 '22 at 02:27

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