相关论文: q-identities of Fu and Lascoux proved by the q-Ric…
We derive several identities involving Ikeda and Naruse's $K$-theoretic Schur $P$- and $Q$-functions. Our main result is a formula conjectured by Lewis and the second author which expands each $K$-theoretic Schur $Q$-function in terms of…
We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.
In this paper we prove some combinatorial identities which can be considered as generalizations and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach…
In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.
In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.
We examine $q-$series related to higher forms. These forms are cubics, quartics, etc. In some points, in the article we add parts from previous works, in such a way, the article be more complete and readable.
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding…
We combinatorially prove Tetranacci, Tetranacci-Fibonacci, and additional identities using only squares and dominoes on a hexagonal double-strip. Some of these are new proofs of old identities, and others we believe have never been seen…
For the Lucas sequence $\{U_{k}(P,Q)\}$ we discuss the identities such as the well-known Fibonacci identities. We also propose a method for obtaining identities involving recurrence sequences. With the help of which we find an interpolating…
We give a $q$-analogue of some binomial coefficient identities of Y. Sun [Electron. J. Combin. 17 (2010), #N20] as follows: {align*} \sum_{k=0}^{\lfloor n/2\rfloor}{m+k\brack k}_{q^2}{m+1\brack n-2k}_{q} q^{n-2k\choose 2} &={m+n\brack…
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…
In this paper, we derive quintic versions of the cubic identities of Farkas and Kra. We believe that our results can be easily generalized to $k$ th power versions,$(k=7,9,11,\ldots).$ Moreover, we investigate the algebraic structure of…
Waldspurger's formula gives an identity between the norm of a torus period and an L-function of the twist of an automorphic representation on GL(2). For any two Hecke characters of a fixed quadratic extension, one can consider the two torus…
Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors.…
Using a cube tiling of $\mathbb{R}^n$ constructed by Lagarias and Shor a tiling proof of three well-known binomial identities related to the Lucas cube is given.
We derive two new identities involving the Bernoulli numbers, the Euler numbers, and the Stirling numbers of the first kind using analytic continuation of a well known identity for the Stirling numbers of the first kind.
We give an identity which is conjectured and proved by using an implementation in Multi-WZ.
In the paper, utilizing respectively the induction, a generating function of the Lah numbers, the Chu-Vandermonde summation formula, an inversion formula, the Gauss hypergeometric series, and two generating functions of the Stirling numbers…
We establish a simple identity and using it we find a new proof of a result of Kloosterman.