Related papers: (Strange) gamma evaluations
The geometry of (2,1) supersymmetric sigma-models is reviewed and the conditions under which they have isometry symmetries are analysed. Certain potentials are constructed that play an important role in the gauging of such symmetries. The…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…
We deduce several curious q-series expansions by applying inverse relations to certain identities for basic hypergeometric series. After rewriting some of these expansions in terms of q-integrals, we obtain, in the limit q -> 1, some…
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…
We calculate some finite and infinite sums containing the digamma function in closed-form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative…
Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which…
In this paper we evaluate integrals of products of gamma functions of Ramanujan type in terms of bilateral hypergeometric series. In cases where the bilateral hypergeometric series are summable, then we evaluate these integral as beta…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
In this paper, we give an algorithm to generate connection formulas of generalized hypergeometric functions ${}_p F_{p-1}$ for degenerated values of parameters. We also show that these connection formulas give a fast method for numerical…
We extend the technique of using the Trapezoidal Rule for efficient evaluation of the Special Functions of Mathematical Physics given by integral representations. This technique was recently used for Bessel functions, and here we treat…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
Hypergeometric functions of complex matrices were introduced by James in multivariate statistics. These special functions play many roles in random matrix theory. The main goal of this paper is to suggest a new use for them as holomorphic…
Infinite series of the type Sum{n=1,infinity}(alpha/2)_n_2F_1(-n, b; gamma; y)/(n n!) are investigated. Closed-form sums are obtained for alpha a positive integer alpha=1,2,3, ... The limiting case of b --> infinity, after y is replaced…
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
We give evaluations in closed form of certain Lehmer-binomial series
We introduce new hypergeometric series expansions of the solutions to the general Heun equation. The form of the Gauss hypergeometric functions used as expansion function differs from that used before. We derive three such expansions and…
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…