相关论文: ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR C…
Different generators of a deformed oscillator algebra give rise to one-parameter families of $q$-exponential functions and $q$-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment…
In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that…
In this paper two important classes of orthogonal polynomials in higher dimensions using the framework of Clifford analysis are considered, namely the Clifford-Hermite and the Clifford-Gegenbauer polynomials. For both classes an explicit…
The method of constructing Hermite trigonometric polynomials, which interpolate the values of a certain periodic function and its derivatives up to (including ) the -th ( ) order in nodes of a uniform grid, is considered. The proposed…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The review of the following results of the Refs. \cite{Sem} - \cite{Ans} is presented: For mixed state light of $N$-mode electromagnetic field described by Wigner function which has generic Gaussian form the photon distribution function is…
We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating…
In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers. As a consequences this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving…
In this paper, we present several explicit formulas of the sums and hyper-sums of the powers of the first (n+1)-terms of a general arithmetic sequence in terms of Stirling numbers and generalized Bernoulli polynomials.
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
A closed form expression for the higher-power coherent states (eigenstates of $a^{j}$) is given. The cases j=3,4 are discussed in detail, including the time-evolution of the probability densities. These are compared to the case j=2, the…
Given an n x n matrix over the ring of differential polynomials F(t)[\D;\delta], we show how to compute the Hermite form H of A, and a unimodular matrix U such that UA=H. The algorithm requires a polynomial number of operations in terms of…
The aim of this paper is to study generalized q-analogs of the well-known q-deformed harmonic oscillators and to connect them with q-Hermite polynomials. We give a construction of the appropriate oscillator-like algebras and show that…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…
While dealing with a class of generalized Bergman spaces on the unit ball, we construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the…
Complementary polynomials of Legendre polynomials are briefly presented, as well as those for the confluent and hypergeometric functions, relativistic Hermite polynomials and corresponding new pre-Laguerre polynomials. The generating…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give formulas for the generating function {equation*} \sigma_{\cone(\J…
We use generating functions to express orthogonality relations in the form of $q$-beta integrals. The integrand of such a $q$-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal
We construct the states that are invariant under the action of the generalized squeezing operator $\exp{(z{a^{\dagger k}}-z^*a^k)}$ for arbitrary positive integer $k$. The states are given explicitly in the number representation. We find…