Related papers: Holonomic Bessel modules and generating functions
Gessel's fundamental and Stembridge's peak functions are the generating functions for (enriched) $P$-partitions on labelled chains. They are also the bases of two significant subalgebras of formal power series, respectively the ring of…
Based on operator algebras commonly used in quantum mechanics some properties of special functions such as Hermite and Laguerre polynomials and Bessel functions are derived.
The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…
We introduce an ${\rm S}_d$-analogue of the hypergeometric Bernoulli polynomials and study their properties. To achieve this goal, we introduce a calculus defined on the simplicial $d$-polytopic numbers. Two definitions of the ${\rm…
The generating functions of the major index and of the flag-major index, with each of the one-dimensional characters over the symmetric and hyperoctahedral group, respectively, have simple product formulas. In this paper, we give a…
It is demonstrated how to use certain family of commutative hypergroups to provide a universal construction of Biane's quantum Bessel processes of all dimensions not smaller than 1. The classical Bessel processes BES$(\delta)$ are…
In this paper, we consider properties of coefficients of a generating functions composition, where the outer function is a logarithmic generating function and the inner function is an ordinary generating function with integer coefficients.…
The aim of this paper is to construct generating functions for some families of special finite sums with the aid of the Newton-Mercator series, hypergeometric series, and $p$-adic integral (the Volkenborn integral). By using these…
We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…
Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on…
The reality of the zeros of the product and cross-product of Bessel and modified Bessel functions of the first kind is studied. As a consequence the reality of the zeros of two hypergeometric polynomials is obtained together with the number…
Based on known definite integrals of Bessel functions of the first kind, we obtain exact solutions to unknown definite integrals using the method of integral transforms from Hankel's transform.
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…
Mellin convolution equations acting in Bessel potential spaces are considered. The study is based upon two results. The first one concerns the interaction of Mellin convolutions and Bessel potential operators (BPOs). In contrast to the…
We derive new identities involving zeros of the Bessel function $J_{\nu}$ and some related functions. These are special cases of more general identities obtained in this note, which might also be of interest.
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad\'e table. We give some properties of…
We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are…
We consider $A$-hypergeometric (or GKZ-)systems in the case where the grading (character) group is an arbitrary finitely generated Abelian group. Emulating the approach taken for classical GKZ-systems in arXiv:math/0406383 that allows for a…