Related papers: The spherical Bessel and Struve functions and oper…
We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…
Two integral operator involving the Appell's functions, or Horn's function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind are expressed in term of generalized Wright function…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
We aim to introduce the generalized multiindex Bessel function $J_{\left( \beta _{j}\right) _{m},\kappa ,b}^{\left( \alpha _{j}\right)_{m},\gamma ,c}\left[ z\right] $ and to present some formulas of the Riemann-Liouville fractional…
Functions like the exponential, Chebyshev polynomials, and monomial symmetric polynomials are preeminent among all special functions. They have simple definitions and can be expressed using easily specified integers like n!. Families of…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for an…
We consider the path approximation of Bessel processes and develop a new and efficient algorithm. This study is based on a recent work by the authors, on the path approximation of the Brownian motion, and on the construction of specific own…
Through the theory of Jack polynomials we give an iterative method for integral formula of Dunkl-Bessel functions of type $A_{N-1}$ and a partial product formula for it.
In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel…
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality…
We use a degeneration of the 1D double affine Hecke algebra and the Dunkl operator to study systematically nonsymmetric Bessel functions and their truncations.
We consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. Explicit representations are obtained for the integrals, building on those in the…
In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations is closed. On basis of these works, we…
The q-Bessel-Macdonald functions of kinds 1, 2 and 3 are considered. Their representations by classical integral are constructed.
This is a survey on recent progress in algebraic deformation theory and the application of algebraic operads to its study. We review the classical homotopical tools in the theory of algebraic operads, namely Koszul duality. We give concrete…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
We try to understand the poles of L-functions via taking a limit in a trace formula. This technique avoids endoscopic and Kim-Shahidi methods. In particular, we investigate the poles of the Rankin-Selberg L-function. Using analytic number…