Related papers: Identities involving Bessel polynomials arising fr…
For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.
In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the…
In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.
In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
In this paper, we study some properties of Sheffer sequences for the powers of Sheffer pairs under umbral composition. From our properties we derive new and interesting identities of Sheffer sequences of special polynomials for the powers…
This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers…
In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.
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.
Some sharp Bessel type inequalities for non-orthonormal families of vectors in inner product spaces are given. Applications for complex numbers are also provided.
The order derivatives of the modified Bessel function of the second kind at s = .5 are obtained as finite expressions of integrals that generalize the exponential integral appearing in the first derivative (Theorem 1.) The derivatives arise…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
In this paper, new integral representations for the Bessel $J$ and $I$ functions were presented and their results were used to derive an expression for the Modified Bessel $K$ function.
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
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…
We derive a collection of identities for bivariate Fibonacci and Lucas polynomials using essentially a matrix approach as well as properties of such polynomials when the variables $x$ and $y$ are replaced by polynomials. A wealth of…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.