相关论文: Mapping Integer Order Neumann Functions To Real Or…

A representation of solutions of the one-dimensional Dirac equation is obtained. The solutions are represented as Neumann series of Bessel functions. The representations are shown to be uniformly convergent with respect to the spectral…

We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.

An explicit expression of the k-th derivative of the Bessel function $J_\nu(z)$, with respect to its order $\nu$, is given. Particularizations for the cases of positive or negative $\nu$ are considered.

We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built…

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,…

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…

In this paper, sums represented in (3) are studied. The expressions are derived in terms of Bessel functions of the first and second kinds and their integrals. Further, we point out the integrals can be written as a Meijer G function.

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…

A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…

In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…

New index transforms, involving the real part of the modified Bessel function 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…

We present a common ground for infinite sums, unordered sums, Riemann/Lebesgue integrals, arc length and some generalized means. It is based on extending functions on finite sets using Hausdorff metric in a natural way.

By studying cohomological quantum mechanics on the punctured plane,we were led to identify (reduced) Bessel functions with homotopic loops living on the plane.This identification led us to correspondence rules between exponentials and…

The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…

In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed…

For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.

Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…

We introduce matching functions as a means of summing heavy-quark logarithms to any order. Our analysis is based on Witten's approach, where heavy quarks are decoupled one at a time in a mass-independent renormalization scheme. The outcome…