Commit 2503f455 authored by Reiner Zorn's avatar Reiner Zorn

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\section{Preface}
This formulary contains a number of useful relations of various generalised hypergeometric functions collected (or in some cases established) by the editor over the years. The term `editor' implies the hope that there will be more contributing authors in the future. At the moment there is only one author and the choice of material may be subjective.
This formulary contains a number of useful relations of various generalised hypergeometric functions collected (or in some cases established) by the editor over the years. The term `editor' implies the hope that there will be more contributing authors in the future. At the moment there is only one author and the choice of material may be subjective. If you wish to contribute please read the last paragraph of this section.
Although best effort is taken to ensure that the relations are correct no effort will be taken to provide mathematically rigorous proofs. These can be obtained in some cases from the cited literature, in other cases may be provided by a more mathematically inclined contributing author. There are basically two dangers arising from this: 1.\ In many cases the conditions of validity of the relations are not stated. But these often also vary for the same statement depending on the source where it is taken from. 2.\ Because some of the functions are complex many-valued, the relations are only fulfilled for a correct choice of the value. For that reason, the reader should make sure by additional tests whether the relations are applicable in the specific intended application.
Because this is a `dynamic' document there will often be the situation that sections are unfinished, or planned but due to workload reasons cannot be implemented immediately. In that case the \bb\ mark (defined as \verb|\bb|) will be used, sometimes extended by a short comment (defined as \verb|\note{}|).
This collection is published on a git repository. The reason for this choice is that it is possible to publish the \LaTeX\ source with full quality, instead of the reduced formula markup used in wikis. Admittedly, it makes collaboration a bit more complicated. If you want to add or change anything you can do this in the \LaTeX\ code and send a pull request. You can also just raise an issue like ``Please add formula (\dots) from reference [\dots]'' and I will include that if it is appropriate. Finally, I would be glad if errors are reported in that way!
This collection is published on a git repository (\url{https://gitlab.com/RZ-FZJ/hypergeom}). The reason for this choice is that it is possible to publish the \LaTeX\ source with full quality, instead of the reduced formula markup used in wikis. Admittedly, it makes collaboration a bit more complicated. If you want to add or change anything you can do this in the \LaTeX\ code and send a pull request. You can also just raise an issue like ``Please add formula (\dots) from reference [\dots]'' and I will include that if it is appropriate. Finally, I would be glad if errors are reported in that way!
\subsection{Notation}
In most cases the notation here will follow the standard notation used in publications about hypergeometric functions. The use of $i$ as index will be avoided. Nevertheless $\i=\sqrt{-1}$ is non-italic for distinction and so are $\d$ and $\e$ in their special meanings. Real and imaginary part are denoted by (old-school) $\Re$ and $\Im$, respectively. A special notation was chosen for the standard `discriminants' constructed from the parameters of the Meijer $G$ function and the Fox $H$ function. They are written in sans s\'erif instead of the standard Greek letters as $\salpha, \sbeta \dots$ (\LaTeX: \verb|\salpha|\dots) to avoid confusion with ordinary symbols.
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