Related papers: Hypergeometric series, truncated hypergeometric se…

We obtain a reflection formula for the Gaussian hypergeometric function of real symmetric matrix argument. We also show that this result extends to the Gaussian hypergeometric function defined over the symmetric cones, and even to…

The theories of hypergeometric functions and modular forms are highly intertwined. For example, particular values of truncated hypergeometric functions and hypergeometric character sums are often congruent or equal to Fourier coefficients…

We geometrically study the Legendre duality relation that plays an important role in statistical physics with the standard or generalized entropies. For this purpose, we introduce dualistic structure defined by information geometry, and…

In this paper, we give the matrix version of Horn's hypergeometric function and its confluent cases. We also discuss the regions of convergence, the system of matrix differential equations of bilateral type, differential formulae and…

HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with…

This survey article (which will appear as a chapter in the book ``Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions'', Springer-Verlag) provides a small collection of basic material on multiple…

As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.

Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…

Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. Often we have hypergeometric functions with indices linear dependent on a small parameter with respect to which…

Using contiguous relations we construct an infinite number of continued fraction expansions for ratios of generalized hypergeometric series 3F2(1). We establish exact error term estimates for their approximants and prove their rapid…

In this paper our aim is to present some Landen inequalities for Gaussian hypergeometric functions, confluent hypergeometric functions, generalized Bessel functions and for general power series. Our main results complement and generalize…

We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…

We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…

We define finite field $A$-hypergeometric functions and show that they are Fourier expansions of families of exponential sums on the torus. For an appropriate choice of $A$, our finite field $A$-hypergeometric function can be specialized to…

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…

We study the combinatorics of two classes of basic hypergeometric series. We first show that these series are the generating functions for certain overpartition pairs defined by frequency conditions on the parts. We then show that when…

Identities involving finite sums of products of hypergeometric functions and their duals have been studied since 1930s. Recently Beukers and Jouhet have used an algebraic approach to derive a very general family of duality relations. In…

We establish some supercongruences for the truncated ${}_2F_1$ and ${}_3F_2$ hypergeometric series involving the $p$-adic Gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated ${}_3F_2$…

We present globally supersymmetric models of gauged scale covariance in ten, six, and four-dimensions. This is an application of a recent similar gauging in three-dimensions for a massive self-dual vector multiplet. In ten-dimensions, we…

We review the hypergeometric function approach to Feynman diagrams. Special consideration is given to the construction of the Laurent expansion. As an illustration, we describe a collection of physically important one-loop vertex diagrams…