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In his work studying the Zeta functions of families of hypersurfaces, Dworkcame upon a one-parameter family of hypersurfaces (now known as \emph{the}Dwork family). These examples were not only useful to Dwork in his study of hisdeformation theory for computing Zeta functions of families, but they have alsoproven to be extremely useful to physicists working in mirror symmetry. Astartling result is that these families are very closely linked tohypergeometric functions. This phenomenon was carefully studied by Dwork andCandelas, de la Ossa, and Rodr\'{i}guez-Villegas in a few special cases. Dwork,Candelas, et.al. observed that, for these families, the differential equationassociated to the Gauss-Manin connection is in fact hypergeometric. We havedeveloped a computer algorithm, implemented in Pari-GP, which can check thisresult for more cases by computing the Gauss-Manin connection and theparameters of the hypergeometric differential equation.

The Dwork Family and Hypergeometric Functions