Related papers: A class of identities relating Whittaker and Besse…
A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…
Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…
In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are established
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…
We consider the monomial expansion of the $q$-Whittaker and modified Hall-Littlewood polynomialsarising from specialization of the modified Macdonald polynomial. The two combinatorial formulas for the latter due to Haglund, Haiman, and…
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…
We present some classes of functions that are defined on the quaternions as solutions for a linear operator that resembles the Cauchy-Riemann conditions. Unlike the Fueter regular functions; in this case the identity function is a solution…
In this paper, a new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions…
We investigate some fundamental properties of a peculiar class of special functions strictly related to Bessel, Anger and Weber functions, whose introduction was originally motivated by linear susceptibility tensor calculations in a hot,…
In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas…
The q-Bessel-Macdonald functions of kinds 1, 2 and 3 are considered. Their representations by classical integral are constructed.
Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_{z}(x), Y_{z}(x)$ and $K_{z}(x)$ are studied. Interesting special cases of these identities are derived, one…
Hypergeometric class equations are given by second order differential operators in one variable whose coefficient at the second derivative is a polynomial of degree $\leq2$, at the first derivative of degree $\leq1$ and the free term is a…
In this note we offer some log-concavity properties of certain functions related to Bessel functions of the first kind and modified Bessel functions of the first and second kind, by solving partially a recent conjecture on the…
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…
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 evaluate $q$-Bessel functions at an infinite sequence of points and introduce a generalization of the Ramanujan function and give an extension of the $m$-version of the Rogers-Ramanujan identities. We also prove several generating…
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of…
By virtue of the technique of integration within an ordered product (IWOP) of operators and the bipartite entangled state representation we derive some new identities about operator Hermite polynomials in both single- and two-variable, we…