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Linear Transformations & the Multivariate Generating Function
Linear Transformations the Multivariate Generating Function
2012/11/23
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 ...
On a completed generating function of locally harmonic Maass forms
locally harmonic Maass forms indefinite theta functions holomorphic projection mock modular forms modular forms
2012/6/21
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...
A Method for Obtaining Generating Function for Central Coefficients of Triangles
Obtaining Generating Function Central Coefficients of Triangles Combinatorics
2012/6/21
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...
A Unified Generating Function of the q-Genocchi Polynomials with their Interpolation Functions
Genocchi numbers and polynomials q-Genocchi numbers and polynomials Number Theory
2011/9/23
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 generating function for the Dirichlet series Lm(s)
Dirichlet series generalized Euler and class number ∧-alternating augmented m-signed permutation r-cubical lattice Springer number
2014/6/3
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...
Two-point generating function of the free energy for a directed polymer in a random medium
Directed polymer Lieb-Liniger Bose gas Kardar-Parisi-Zhang equation
2010/11/24
We consider a 1+1 dimensional directed continuum polymer in a Gaussian delta-correlated space-time random potential. For this model the moments (= replica)of the partition function, Z(x, t), can be ex...
Moment generating function of the bivariate generalized exponential distribution
bivariate generalized exponential distribution joint and marginal moments
2010/9/17
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...
Variational Description for the Generating Function Method of First Kind
generating function method multisymplectic
2007/12/11
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 ...