Less simple contiguous function relations for hypergeometric functions

Contiguous relations of hypergeometric series

The 15 Gauss contiguous relations for 2F1 hypergeometric series imply that any three 2F1 series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We prove several properties of coefficients of these general contiguous relations, and use the results to propose effective ways to compute contiguous relations. We also di...

Contiguous relations for 2F1 hypergeometric series

ess as: 2), http: athemat s.2012.0 Abstract Two Gauss functions are said to be contiguous if they are alike except for one pair of parameters, and these differ by unity. Contiguous relations are of great use in extending numerical tables of the function. In this paper we will introduce a new method for computing such types of relations. a 2012 Egyptian Mathematical Society. Production and hosti...

GG-functions and their relations to A-hypergeometric functions

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...

Twisted period relations associated with con uent hypergeometric functions

1 Introduction Formulas of intersection numbers were given in [1] and [4] for twisted de-Rham cohomology groups and twisted homology groups dened by the connection r ! = d + ! associated with a 1-form ! with simple poles on the projective line P. In this paper, we present a denition of intersection pair-ing and a formula of intersection numbers between twisted homology groups associated with a ...

Hypergeometric Functions