We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions. We also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank.

In [Koepf (1992)] it was shown how for a given holonomic function a representation as a formal power series of hypergeometric type can be determined algorithmically. This algorithm – that we call FPS algorithm (Formal Power Series) – combines three steps to obtain the desired representation. The authors implemented this algorithm in the computer algebra system Maple as c̀onvert/FormalPowerSeries...

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric functionΦ1 of matrix arguments. Further, a bimatrix variate generalization...

The left hand side (or A–side) of this identity was a generating series for the numbers n(d) of rational curves of various degrees d lying on a smooth quintic hypersurface in P. The right hand side (B–side) was a certain hypergeometric function. The Mirror Identity states that the two functions become identical after an explicit change of variables which is defined as a quotient of two hypergeo...