相关论文: On the interlacing property for zeros of Bessel fu…

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…

This paper investigates a generalized interlacing property between Bessel functions, particularly $J_\nu$ and $J_\mu$, where the difference $|\nu-\mu|$ exceeds $2$. This interlacing phenomenon is marked by a compensatory interaction with…

Necessary and sufficient conditions for the interlacing of the zeros of cylinder functions and their derivatives of different orders are given.

We prove that for $\nu>n-1$ all zeros of the $n$th derivative of Bessel function of the first kind $J_{\nu}$ are real and simple. Moreover, we show that the positive zeros of the $n$th and $(n+1)$th derivative of Bessel function of the…

We unify the three distinct inequality sequences (Abramowitz ans Stegun (1972) [1,9.5.2]) of positive real zeros of Bessel functions into a single one.

This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…

It is well known that the zeros of orthogonal polynomials interlace. In this paper we study the case of multiple orthogonal polynomials. We recall known results and some recursion relations for multiple orthogonal polynomials. Our main…

We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior…

The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.

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…

This paper deals with the study of the zeros of the big $q$-Bessel functions. In particular, we prove a new orthogonality relations for this functions similar to the one for the classical Bessel functions. Also we give some applications…

We derive new identities involving zeros of the Bessel function $J_{\nu}$ and some related functions. These are special cases of more general identities obtained in this note, which might also be of interest.

The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…

We introduce the concept of piecewise interlacing zeros for studying the relation of root distribution of two polynomials. The concept is pregnant with an idea of confirming the real-rootedness of polynomials in a sequence. Roughly…

The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…

We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular…

The purpose of this paper is twofold. One is to investigate the properties of the zeros of cross-products of Bessel functions or derivatives of ultraspherical Bessel functions, as well as the properties of the zeros of the derivative of the…

We study the distribution of zeros of general solutions of the Airy and Bessel equations in the complex plane. Our results characterize the patterns followed by the zeros for any solution, in such a way that if one zero is known it is…

We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover…