Related papers: Identities involving Bessel polynomials arising fr…
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the…
In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate…
New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a composita and a Bell polynomial is demonstrated. Main…
The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…
We discuss closed-form formulas for the (n; k)-th partial Bell polynomials derived in Cvijovic. We show that partial Bell polynomials are special cases of weighted integer compositions, and demonstrate how the identities for partial Bell…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
We have solved a number of holonomic PDEs derived from the Bessel modules which are related to the generating functions of classical Bessel functions and the difference Bessel functions recently discovered by Bohner and Cuchta. This…
In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.
We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions.…
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.
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…
We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…
In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of…
We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as…
Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…
In this paper, we study the degenerate central complete and incomplete Bell polynomials which are degenerate versions of the recently introduced central complete and incomplete Bell polynomials and also central analogues for the degenerate…
We derive an identity that relates a class of multiple integrals involving Vandermonde polynomials to divided differences. Alternatively the identity can be viewed as an integral formula for divided differences. As part of the derivation we…