Related papers: On a new result for the hypergeometric function
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional…
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
We derive new identities involving zeros of the Bessel function $J_{\nu}$ and some related functions. These are special cases of more general identities obtained in this note, which might also be of interest.
We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within…
The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
In this note we state (with minor corrections) and give an alternative proof of a very general hypergeometric transformation formula due to Slater. As an application, we obtain a new hypergeometric transformation formula for a ${}_5F_4(-1)$…
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
The beta integral method proved itself as a simple nonetheless powerful method of generating hypergeometric identities at a fixed argument. In this paper we propose a generalization by substituting the beta density with a particular type of…
A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
Gaussian functions are commonly used in different fields, many real signals can be modeled into such form. Research aiming to obtain a precise fitting result for these functions is very meaningful. This manuscript intends to introduce a new…
We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the…
The objective of this short note is to provide two closed-form evaluations for the generalized hypergeometric function $_4F_3$ of the argument $\frac1{16}$. This is achieved by means of separating a generalized hypergeometric function…
We naturally obtain some combinatorial identities finding the difference analogs of hyperbolic and trigonometric functions of order $n.$ In particular, we obtain the identities connected with the proved in the paper the addition formulas…