Related papers: On an identity for H-function
Despite all its well-known flaws and calls for its dismissal, the notorious $h$-index is still used in many instances when awarding grants, or promoting and hiring scientists. To address this, I set out to devise a better index, with the…
The citation distribution of a researcher shows the impact of their production and determines the success of their scientific career. However, its application in scientific evaluation is difficult due to the bi-dimensional character of the…
We establish some functional identities of theta functions, an elementary proof of classical fourth-order identities, Landen transformations, and q series from the eigenvectors of the discrete Fourier transform. Also, we derive connection…
We prove an identity about partitions with a very elementary formulation. We had previously conjectured this identity, encountered in the study of shifted Jack polynomials (math.CO/9901040). The proof given is using a trivariate generating…
In the process of studying a conjecture of Holly M. Green and Martin W. Liebeck, we obtain two interesting identities by elementary methods, one is a combinatorial identity, and the other is a number theoretic identity.
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Almost automorphy in the context of hyperfunctions is the main aim of this work. We give different equivalent definitions of almost automorphic hyperfunctions and then we study this class of hyperfunctions.
Let $g$ be an additive map on a division ring $D$. In this paper, we study the functional identity $G_{1}(y)g(y)G_{2}(y) = H(y)$, where $G_{1}(Y), G_{2}(Y)$, $H(Y)$ are generalized polynomials in $D_{G}[Y]$ such that both $G_{1}(Y)$ and…
Based on the work of A. Vershik, we introduce two new combinatorial identities. We show how these identities can be used to prove a new hook-content identity. The main motivation for deriving this identity was a particular optimization…
The aim of this research paper is to obtain explicit expressions of (i) $ {}_1F_1 \left[\begin{array}{c} \alpha \\ 2\alpha + i \end{array} ; x \right]. {}_1F_1\left[ \begin{array}{c} \beta \\ 2\beta + j \end{array} ; x \right]$ (ii)…
Given a convergent sequence of nodes we present a one-dimensional-holomorphic-function version of the Newton interpolation method of polynomials. It also generalises the Taylor and the Laurent formula. In other words, we present an…
The primary purpose of this paper is to provide a survey of properties, values, identities, and generalizations of the Rogers--Ramanujan continued fraction, which is closely related to the Rogers--Ramanujan identities. Many of these results…
Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall-Littlewood functions. We also give a determinant formula for the Macdonald functions.
For a certain function $J(s)$ we prove that the identity $$\frac{\zeta(2s)}{\zeta(s)}-\left(s-\frac{1}{2}\right)J(s)=\frac{\zeta(2s+1)}{\zeta(s+1/2)}, $$ holds in the half-plane Re$(s)>1/2$ and both sides of the equality are analytic in…
In this paper, we introduce the normalized Shintani L-function of several variables by an integral representation and prove its functional equation. The Shintani L-function is a generalization to several variables of the Hurwitz-Lerch zeta…
In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.
We introduce a general method, named the h-function method, to unify the constructions of level-alpha exact test and 1-alpha exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate…
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…
Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions…