相关论文: Identities involving elementary symmetric function…

In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…

In this paper, we investigate some new symmetric identities for the q-Euler polynomials under the symmetric group of degree n which are derived from fermionic p-adic q-integrals on Zp.

The partition functions $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, and $Q(n,m,p)$, the number of integer partitons of $n$ into exactly $m$ distinct parts with each part at most…

In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.

We present a number of identities involving standard and associated Laguerre polynomials. They include double-, and triple-lacunary, ordinary and exponential generating functions of certain classes of Laguerre polynomials.

We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently…

We present a systematic approach to thermodynamical identities and illustrate the power of these methods by displaying Mathematica notebooks to deal with a large variety of such identities. In concrete examples these can involve rather…

In this paper, we study some symmetric properties of the multiple q-Euler zeta function. From these properties, we derive several identities of symmetry for the (h;q)-extension of higher-order Euler polynomials.

We obtain some Bailey pairs associated with indefinite quadratic forms with the $\beta_n$ connected to a finite sum. A new general identity is given, which provides identities for $q$-hypergeometric series, including mock theta functions.

In this paper we derive new identities satisfied by Chebyshev polynomials of the first kind and big q-Jacobi polynomials. An immediate benefit of the derived identities is the achievement of closed-form expressions for the Laurent…

We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.

We present an elementary identity for the cyclotomic polynomials $\Phi_n(X)$ which reflects a kind of multiplicative property of $\Phi_n(X)$ as a function of $n$, and we explore its connections with the properties of other arithmetical…

We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…

The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms. The aim of this…

Recently, Kim-Kim Introduced some interesting identities of symmetry for q-Bernoulli polynomials under symmetry group of degree n. In this paper, we study the degenerate q-Euler polynomials and derive some identities of symmetry for these…

It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to…

In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.

In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.

We prove polynomial boson-fermion identities for the generating function of the number of partitions of $n$ of the form $n=\sum_{j=1}^{L-1} j f_j$, with $f_1\leq i-1$, $f_{L-1} \leq i'-1$ and $f_j+f_{j+1}\leq k$. The bosonic side of the…

Some examples of naturally arising multisum $q$-series which turn out to have representations as fermionic single sums are presented. The resulting identities are proved using transformation formulas from the theory of basic hypergeometric…