Related papers: Identities involving elementary symmetric function…
We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in terms of the series involving hyperbolic functions, digamma function, Bernoulli numbers etc. In this version, inaccuracies…
Presented are polynomial identities which imply generalizations of Euler and Rogers--Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by…
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
A family of general integral identities is derived and several applications of physical interest are presented
The article describes interesting nonlinear differential identities satisfied by standard exponential and trigonometric functions, which appeared as byproducts of medical imaging research. They look like some kind of non-commutative…
We give some new identities for (h; q)-Genocchi numbers and polynomials by means of the fermionic p-adic q-integral on Zp and the weighted q-Bernstein polynomials.
A series of bilinear identities on the Schur symmetric functions is obtained with the use of Pluecker relations.
We obtain formulas for the coefficients of positive and negative powers of a partial theta function.
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…
Recently N.Jing discovered a certain combinatorial identity from validity of the Serre relations in some vertex representations of quantum Kac-Moody algebras. We generalize this identity, in particular, extending it from polynomials to…
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.
By applying an integral representation for $q^{k^{2}}$ we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of $q$-functions and polynomials that…
This paper presents new identities expressing the terms of Fibonacci, Lucas, and generalized Fibonacci sequences with multiple indices through powers of Lucas numbers and binomial coefficients. The obtained formulas rely on the application…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius-Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of…
Families of operator identities appeared as a consequence of an existence of finite-dimensional representation of (super) Lie algebras of first-order differential operators and $q$-deformed (quantum) algebras of first-order…
In the article [11] of L. Kunyansky a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the…
We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…