相关论文: A new identity linking coefficients of a certain c…

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.

Let A be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group G. Here we study a growth function related to the graded polynomial identities satisfied by A by computing the exponential rate of…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

In our previous work, a unified description as polynomial Hamiltonian systems was established for a broad class of the Schlesinger systems including the sixth Painleve equation and Garnier systems. The main purpose of this paper is to…

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 paper, we aim to obtain a representation of Humbert's hy- pergeometric function in a series of Gauss's function 2F1. A few interesting results have also been deduced as special case of our main findings.

We consider certain functional identities on the matrix algebra $M_n$ that are defined similarly as the trace identities, except that the "coefficients" are arbitrary polynomials, not necessarily those expressible by the traces. The main…

We establish two binomial coefficient--generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of…

Recently, Chan, Cooper and Sica conjectured two congruences for coefficients of classical 2F1 hypergeometric series which also arise from power series expansions of modular forms in terms of modular functions. We prove these two congruences…

By using Fourier transforms of two symmetric sequences of finite orthogonal polynomials, we introduce two new classes of finite orthogonal functions and obtain their orthogonality relations via Parseval's identity.

In the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes extend the well…

In this work we consider a family of function classes constructed by means of the Gauss hypergeometric function $_2F_1(1,1;2;z) =-\frac{\log(1-z)}{z}$. We demonstrate that this family, in fact, constitutes classes of analytic functions…

We study selfadjoint functors acting on categories of finite dimensional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint functors satisfying several easy relations, in…

A new polynomial identity is found for Dickson polynomials in characteristic 2. The identity is used to prove that the two polynomials $x^{q+1}+x+1/a$ and $C(x)+a$ have the same splitting field over $F$, where $F$ is a field of…

This paper describes a method to find a connection between combinatorial identities and hypergeometric series with a number of examples. Combinatorial identities can often be written as hypergeometric series with unit argument. In a number…

We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra,…

We revisit the phenomenon where, for certain domains $D$, if the squeezing function $s_D$ extends continuously to a point $p\in \partial{D}$ with value $1$, then $\partial{D}$ is strongly pseudoconvex around $p$. In $\mathbb{C}^2$, we…

We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de Rham (co)homologies. The identity also…

We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…

We study polynomial identities satisfied by the mutation product $xpy - yqx$ on the underlying vector space of an associative algebra $A$, where $p, q$ are fixed elements of $A$. We simplify known results for identities in degree $4$,…