We extend the well-known results about the process of confluence for the Gauss hypergeometric differential equation to the case of general hypergeometric systems. We see that the process of confluence comes from the geometry of the set of regular elements of the Lie algebra of complex general linear group. As a consequence, we give a geometric and group-theoretic view on the process of confluen...

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...

The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Clausenian hypergeometric 3F2 functions and polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Clausenian hypergeometric polynomials: 3F2(−n, τn+ a, b; τn+ c,−n+ d; z), where n is a nonnegative integer. Some families o...

The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formul\ae\ Gauss' hypergeometric functions. We define tau-function such as generating function extended symplectomorphism, using an idea recently developed. This formulation allows us to determine dependence on data. Using explicit solution problem, then explic...