Related papers: On an identity for H-function
In 2002 Zhi-Wei Sun [Integers 2(2002)] published a curious identity involving binomial coefficients. In this paper we present a generalization of the identity.
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
The aim of the paper is the proof of new identities for the constant in the Mertens product for arithmetic progressions. We deal with the problem of the numerical computation of these constants in another paper.
We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function $G(z;\tau)$. Second, we derive an algorithm for numerically…
In this paper, a general integral identity for twice differentiable functions is derived. By using of this identity, the author establish some new estimates on Hermite-Hadamard type and Simpson type inequalities for s-convex via Riemann…
In this paper, a general integral identity for a twice differentiable functions is derived. By using of this identity, the author establishes some new Hermite-Hadamard type and Simpson type inequalities for differentiable…
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
The Hirsch function of a given continuous function is a new function depending on a parameter. It exists provided some assumptions are satisfied. If this parameter takes the value one, we obtain the well-known h-index. We prove some…
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the second kind, the degenerate $r$-Stirling numbers of the second kind, the degenerate Stirling…
This paper is an annotated list of transformation properties and identities satisfied by the four theta functions $\theta _1$, $\theta _2$, $\theta _3$, $\theta _4$ of one complex variable, presented in a ready-to-use form. An attempt is…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
The h-index is a mainstream bibliometric indicator, since it is widely used in academia, research management and research policy. While its advantages have been highlighted, such as its simple calculation, it has also received widespread…
During the course of an ongoing work on the small-$x$ behaviour of parton distribution functions, some identities have been found which involve Stirling numbers of the first and the second kind, as well as binomial coefficients. Without any…
The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.
The present work proposes analytical solutions for the integral of bivariate Fox H-function in combination with algebraic, exponential, and complementary error functions. In addition, the work also presents the derivative identities with…
I introduce a decomposition of the h-index, which is nowadays the leading criterion to assess the relevance of a scientist in his/her research field. According to the proposed decomposition, the h-index is the product of two indicators, the…
Some conjectures on partition hook lengths, recently stated by the author, have been proved and generalized by Stanley, who also needed a formula by Andrews, Goulden and Jackson on symmetric functions to complete his derivation. Another…
Given ideals $I,J$ of a noetherian local ring $(R, \mathfrak m)$ such that $I+J$ is $\mathfrak m$-primary and a finitely generated $R$-module $M$, we associate an invariant of $(M,R,I,J)$ called the $h$-function. Our results on…