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This note examines linear combinations of multi-indexed sequences and derives the multivariate generating function of such a linear combination in terms of the original sequence's m.g.f. Applications ...
While investigating the Doi-Naganuma lift, Zagier defined integral weight cusp forms $f_D$ which are naturally defined in terms of binary quadratic forms of discriminant $D$. It was later determined b...
We consider problems of obtaining a generating function for the central coefficients of triangle $T(n,k)$, which is given by expression $[xG(x)]^k=\sum_{n\geqslant k} T(n,k)x^n$, $G(0)\neq 0$. We prov...
Abstract: The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extens...
The Dirichlet series Lm(s) are of fundamental importance in number theory. Shanks defined the generalized Euler and class numbers in connection with the Dirichlet series, denoted by {sm, n}n≥0. We obt...
Recently a new distribution, named a bivariate generalized exponential (BVGE) distribution has been introduced by Kundu and Gupta (2008). In this paper we obtain joint moments and the moment generatin...
We propose the variational description of generating function approach of first kind for Hamiltonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any ...

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