Related papers: Series with Hermite Polynomials and Harmonic Numbe…

An observation on Hall-Littlewood polynomials.

We find various series that involves the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function $_pF_q$ approach, our method utilizes a straightforward…

Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from…

This paper is a survey on the study of the behaviour of the composition of polynomials on the computation of Gr\"obner bases. This survey brings together some works published between 1995 and 2007. The authors of these papers gave answers…

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…

In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.

In this paper we get two new classes of regular sequences in the polynomial ring over the field of complex numbers.

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…

This paper explores the operational principles and monomiality principle that significantly shape the development of various special polynomial families. We argue that applying the monomiality principle yields novel results while remaining…

Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, and in some cases simpler, expressions to those recently…

In this paper we exhibit and study a novel class of exceptional Krall orthogonal polynomials of Hermite type. This means that the polynomials in question are (i) orthogonal with respect to a Hermite-type weight; (ii) are the eigenfunctions…

The contents of the paper is now covered in two separate papers arXiv:0904.2188 and arXiv:0904.2602. Please refer to those. Note that you can still access the original version arXiv:0711.4082v1.

We study the orthogonal complement of the Hilbert subspace considered by by van Eijndhoven and Meyers in [J. Math. Anal. Appl. 146 (1990), no. 1, 89--98} and associated to holomorphic Hermite polynomials. A polyanalytic orthonormal basis is…

It was discovered recently by Griffin, Ono, Rolen and Zagier that the Jensen polynomials associated to many sequences have Hermite polynomial limits. We develop this theory in detail, based on the log-polynomial property which is a…

The classical hypergeometric summation theorems are exploited to derive several striking identities on harmonic numbers including those discovered recently by Paule and Schneider (2003).

In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…

The content of this paper is incorporated into hep-th/9805093

We introduce two classes of $(p,q)$-It\^o--Hermite polynomials, the post-quantum analogs of the $q$-It\^o--Hermite polynomials introduced recently by Ismail and Zhang. We study their basic properties such as their operational formulas of…

Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…

We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the…