The roots of the general equation of degree n satisfy an A-hypergeometric system of diierential equations in the sense of Gel'fand, Kapranov and Zelevinsky. We construct the n distinct A-hypergeometric series solutions for each of the 2 n?1 triangulations of the Newton segment. This works over any eld whose characteristic is relatively prime to the lengths of the segments in the triangulation. ...

The multiplicate form of Gould–Hsu’s inverse series relations enables to investigate the dual relations of the Chu–Vandermonde–Gauß’s, the Pfaff–Saalschütz’s summation theorems and the binomial convolution formula due to Hagen and Rothe. Several identitity and reciprocal relations are thus established for terminating hypergeometric series. By virtue of the duplicate inversions, we establish sev...

In [1] I.M.Gelfand introduced the conception of hypergeometric functions, associated with the Grassmanian Gk,n of k-dimensional subspaces in C . The class of these functions includes many classical hypergeometric functions as particular cases. Series of consequent papers of I.M.Gelfand and his coathors ([2]–[6]) are devoted to the theory of these functions. In particular, the paper [4] is devot...

Series and integrals of hypergeometric type have many applications in mathematical physics. Investigation of the corresponding special functions can therefore be relevant for various computations in theoretical models of reality. Bailey chains provide powerful tools for generating infinite sequences of summation or transformation formulas for hypergeometric type series. For a review of the corr...

Based on the blossoming theory, in this work we develop a new method for deriving Hermite-Padé approximants of certain hypergeometric series. Its general principle consists building identities generalising Hermite identity exponentials, and then applying their blossomed versions to appropriate tuples simultaneously produce explicit expressions integral representations corresponding remainders. ...