Related papers: Indefinite Integrals of Spherical Bessel Functions
A finite transformation method is introduced. This method is equivalent to the $Z$ transform method to a certain extent but generalizes it. By applying the presented method to the Bessel functions, it is possible to solve related ordinary…
A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…
In this paper, we determine necessary and sufficient conditions for the generalized Bessel function to be in certain subclasses of starlike and convex functions. Also, we obtain several corollaries as special cases of the main results,…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial,…
We study how the orbits of the singularities of the inverse of a meromorphic function prescribe the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions…
The Humbert-Bessel are multi-index functions with various applications in electromagnetism. New families of functions sharing some similarities with Bessel functions are often introduced in the mathematical literature, but at a closer…
Similar to the associated Legendre functions, the differential equation for the associated Bessel functions $B_{l,m}(x)$ is introduced so that its form remains invariant under the transformation $l\rightarrow -l-1$. A Rodrigues formula for…
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…
This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of…
We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
We unify several Bellman function problems into one setting. For that purpose we define a class of functions that have, in a sense, small mean oscillation (this class depends on two convex sets in $\mathbb{R}^2$). We show how the unit ball…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
The paper presents a new and simple range characterization for the spherical mean transform of functions supported in the unit ball in even dimensions. It complements the previous work of the same authors, where they solved an analogous…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
Indefinite inner product spaces of entire functions and functions analytic inside a disk are considered and their completeness studied. Spaces induced by the rotation invariant reproducing kernels in the form of the generalized…
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…
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…