Related papers: On digamma series convertible into hypergeometric …
Embedding Feynman integrals in Grassmannians, we can write Feynman integrals as some finite linear combinations of generalized hypergeometric functions. In this paper we present a general method to obtain Gauss relations among those…
In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler $\Gamma$-functions and exponential functions of linear functions of the hypergeometric parameters. They include some classical…
Based on $k$-gamma and $k$-digamma functions, we show four series expansions to the Furdui-type integral related to Riemann zeta function and hypergeometric function, and also present some new identities, series expansions and inequalities…
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…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
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…
We introduce a natural method of computing antiderivatives of a large class of functions which stems from the observation that the series expansion of an antiderivative differs from the series expansion of the corresponding integrand by…
In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
We continue our study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we apply the approach of obtaining iteratated solutions to…
A new expansion for integral powers of the hypergeometric function corresponding to a special case of the incomplete beta function is summarized, and consequences, including two new sums involving digamma (psi) functions are presented.
We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.
In this very short note we will derive an inequality for a class of entire functions including all the confluent basic hypergeometric series and an inequality for a class of meromorphic functions including theta functions.
In \cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\cdots]$ using the Teichm\"{u}ller character of finite fields and quotients of the $p$-adic gamma function. This function extends hypergeometric functions over finite fields to the…
Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of…
The standard literature on special functions contains a lot of hypergeometric identities involving products and quotients of gamma functions, but still the occurrence of such identities is a sporadic phenomenon. This is because the…
We prove hypergeometric type summation identities for a function defined in terms of quotients of the $p$-adic gamma function by counting points on certain families of hyperelliptic curves over $\mathbb{F}_{q}$. We also find certain special…
The main objective of the present article is to make interconnection between the Generalized Hyergeometric series and some subclasses of normalized analytic functions with positive(Tailor's) coefficients in the open unit disc $\mathbb{D}…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain…