Related papers: A General Integral Identity
In this paper we introduce two general identities relating Eisenstein series on split classical groups, as well as double covers of symplectic groups. The first identity can be viewed as an extension of the doubling construction introduced…
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…
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
We give a general identity relating Eisenstein series on general linear groups. We do it by constructing an Eisenstein series, attached to a maximal parabolic subgroup and a pair of representations, one cuspidal and the other a character,…
By counting the numbers of periodic points of all periods for some interval maps, we obtain infinitely many new congruence identities in number theory.
The aim of this research paper is to demonstrate how one can obtain eleven new and interesting hypergeometric identities (in the form of a single result) from the old ones by mainly applying the well known beta integral method which was…
The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised $_6\phi_5$ series.
The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…
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…
In this article we shows some results about algebra with the group of units having special polynomial identity.
Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…
In 2007 V. Zhuravlev discovered a family of identities concerning integer parts which are satisfied by the number $\frac{\sqrt{5}+1}{2}$. Some of these identities turned out to be characterization properties of the number…
The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less…
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
It gives some new forms of General Neron Desingularization and new applications.
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and…
We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…
Two new generalized Fibonacci number summation identities are stated and proved, and two other new generalized Fibonacci number summation identities are derived from these, of which two special cases are already known in literature.