Related papers: Some Generalized Multi-sum Chu-Vandermonde Identit…
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.
We give generalizations of a finite version of Euler's pentagonal number theorem and of a q-identity of Gauss.
The multiplicate form of Gould--Hsu's inverse series relations enables to investigate the dual relations of the Chu-Vandermonde-Gau{\ss}'s, the Pfaff-Saalsch\"utz's summation theorems and the binomial convolution formula due to Hagen and…
The "2-variable general-$\lambda$-matrix polynomials (2VG$\lambda$MP)" is a new family of matrix polynomials, introduced and studied in this article. These matrix polynomials are constructed using umbral and symbolic methods. We delve into…
In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…
We prove certain Nahm-type sum representations for the (odd modulus) Andrews-Gordon identities, the (even modulus) Andrews-Bressoud identities, and Rogers' false theta functions. These identities are motivated on one hand by a recent work…
We discuss closed-form formulas for the (n; k)-th partial Bell polynomials derived in Cvijovic. We show that partial Bell polynomials are special cases of weighted integer compositions, and demonstrate how the identities for partial Bell…
Motivated by the recent work of Chu [Electron. J. Combin. 17 (2010), #N24], we give simple proofs of Jensen's identity $$ \sum_{k=0}^{n}{x+kz\choose k}{y-kz\choose n-k} =\sum_{k=0}^{n}{x+y-k\choose n-k}z^k, $$ and Chu's and Mohanty-Handa's…
Based on Jensen formulae and the second kind of Chebyshev polynomials, another proof is presented for an extension of a curious binomial identity due to Z. W. Sun and K. J. Wu.
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…
In this paper, we give some identities of symmetry for the generalized degenerate Euler polynomials attached to chi which are derived from the symmetric properties for certain fermionic p-adic integrals on Zp.
Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first…
Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…
We provide combinatorial tools inspired by work of Warnaar to give combinatorial interpretations of the sum sides of the Andrews-Gordon and Bressoud identities. More precisely, we give an explicit weight- and length-preserving bijection…
We elaborate on the recent suggestion to consider averaging of Cauchy identities for the Schur functions over power sum variables. This procedure has apparent parallels with the Borel transform, only it changes the number of combinatorial…
Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely…
We study two identities involving roots of unity and determinants of Hermitian matrices which have been recently proved by using the famous eigenvector-eigenvalue identity for normal matrices. In this paper, we extend these identities to a…
Motivated by the recent work of William Y.C. Chen, in which he presents a way to solve cubic equations by considering the identity of Sylvester, we investigate the solutions obtained in this way. It leads us to a unified expression of the…
In this note, we obtain some identities for the generalized Fibonacci polynomial by using the Q(x) matrix. These identities including the Cassini identity and Honsberger formula can be applied to some polynomial sequences, such as Fibonacci…
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the…