Some recent results on the zeros of Bessel functions and orthogonal polynomials

DOI10.1016/S0377-0427(00)00635-XzbMath0989.33004OpenAlexW1970297574MaRDI QIDQ5946584

Árpád Elbert

Publication date: 22 July 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00635-x

zbMATH Keywords

inequalitieszerosclassical orthogonal polynomialsBessel functionsAiry function

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items

A connection between ultraspherical and pseudo-ultraspherical polynomials, Árpád Elbert, 1939--2001: A memorial tribute., Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials, On the zeros and turning points of special functions., On a conjecture regarding the extrema of Bessel functions and its generalization, Zeros of combinations of Bessel functions and the mean charge of graphene nanodots, The finite Hankel transform operator: some explicit and local estimates of the eigenfunctions and eigenvalues decay rates, Zeros of Gegenbauer and Hermite polynomials and connection coefficients, On exact Pleijel's constant for some domains, Boundary controllability for a coupled system of parabolic equations with singular potentials, Stable source reconstruction from a finite number of measurements in the multi-frequency inverse source problem, Collective interlacing and ranges of the positive zeros of Bessel functions, Pointwise controllability for degenerate parabolic equations by the moment method, \((p,q)\)-extended Bessel and modified Bessel functions of the first kind, Controllability properties of degenerate pseudo-parabolic boundary control problems, Sharp bounds for the extreme zeros of classical orthogonal polynomials, Asymptotic relation for zeros of cross-product of Bessel functions and applications, Spurious eigenvalue-free algorithms of the method of fundamental solutions for solving the Helmholtz equation in bounded multiply connected domains, Studies on the zeros of Bessel functions and methods for their computation, On the L 2 Markov Inequality with Laguerre Weight, Fast Expansion into Harmonics on the Disk: A Steerable Basis with Fast Radial Convolutions, Symmetry and monotonicity results for solutions of semilinear PDEs in sector-like domains, Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions, On the spectrum of a mixed-type operator with applications to rotating wave solutions, Energy stability of droplets and dry spots in a thin film model of hanging drops, Continuous ranking of zeros of special functions, Creating Band Gaps in Periodic Media, On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics, A note on band-limited minorants of an Euclidean ball, A singular Sturm-Liouville equation under homogeneous boundary conditions, Unnamed Item, On the controllability of a class of degenerate parabolic equations with memory, On the Largest Critical Value of $T_n^(k)$, On dry spot and droplet solutions for thin films on the plane, Zeros of classical orthogonal polynomials of a discrete variable, Studies on the zeros of Bessel functions and methods for their computation. II: Monotonicity, convexity, concavity, and other properties, A Pohožaev type identity and its application to uniqueness of positive radial solutions of Brezis-Nirenberg problem on an annulus, Trapped modes in angular joints of 2D waveguides, Locating and computing in parallel all the simple roots of special functions using PVM, The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals, Cubic Nonlinear Schrödinger Equation on Three Dimensional Balls with Radial Data, On the \({ L}^{ p}\) norm of the torsion function, Asymptotics and exact formulas for Zagier polynomials, On the curves of zeros of Lommel functions of two variables, Monotonic sequences related to zeros of Bessel functions, Zeros' distribution of the first kind Bessel functions, FINITE DIMENSIONAL QUANTIZATIONS OF THE (q,p) PLANE: NEW SPACE AND MOMENTUM (OR QUADRATURES) INEQUALITIES, Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications, Rome, Italy, June 18--22, 2001. Dedicated to the memory of Professor Árpád Elbert, Diophantine Gaussian excursions and random walks, Boundary controllability for a coupled system of degenerate/singular parabolic equations, On the zeros ofJ_ν″′(x), Proofs of Two Conjectures on the Real Zeros of the Cylinder and Airy Functions, Unique continuation principles for a higher order fractional Laplace equation, The asymptotically linear Hénon problem, The electrostatic properties of zeros of exceptional Laguerre and Jacobi polynomials and stable interpolation, Application of Krein's series to calculation of sums containing zeros of the Bessel functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monotonicity and concavity properties of zeros of Bessel functions
• On the zeros of derivatives of Bessel functions
• An asymptotic relation for the zeros of Bessel functions
• Upper bounds for the zeros of ultraspherical polynomials
• Differential inequalities for the positive zeros of Bessel functions
• Padé-type approximants of \(\exp(-z)\) whose denominators are \((1+z/n)^ n\)
• On the variation with respect to a parameter of zeros of Bessel and q- Bessel functions
• An approximation for the zeros of Bessel functions
• Asymptotics for the \(n\)th-degree Laguerre polynomial evaluated at \(n\)
• A differential inequality for the positive zeros of Bessel functions
• Monotonicity properties of the zeros of ultraspherical polynomials
• Strong asymptotics for Jacobi polynomials with varying weights
• On the control of a circular membrane. I
• On the zeros of Jacobi polynomials
• An upper bound for the zeros of the derivative of Bessel functions
• The real zeros of the derivatives of cylinder functions of negative order
• Bounds for the small real and purely imaginary zeros of Bessel and related functions
• Improving the asymptotics for the greatest zeros of Hermite polynomials
• The zeros of the third derivative of Bessel functions of order less than one
• Uniform upper and lower bounds on the zeros of Bessel functions of the first kind
• On a conjecture concerning monotonocity of zeros of ultraspherical polynomials
• ``Best possible upper bounds for the first two positive zeros of the Bessel function \(J_ \nu (x)\): The infinite case
• ``Best possible upper bounds for the first positive zeros of Bessel functions -- the finite part
• On the Zeros of Jacobi Polynomials P ( | alpha n , | beta n ) n (X)
• A Series Expansion for the First Positive Zero of the Bessel Functions
• On the Square of the Zeros of Bessel Functions
• A differential equation for the zeros of bessel functions
• On Estimates for the Weights in Gaussian Quadrature in the Ultraspherical Case
• FURTHER RESULTS ON THE ZEROS OF BESSEL FUNCTIONS
• On the Convexity of the Zeros of Bessel Functions
• Monotonicity Properties of the Zeros of Bessel Functions
• Inequalities and Numerical Bounds for Zeros of Ultraspherical Polynomials
• A Monotonic Property for the Zeros of Ultraspherical Polynomials
• On the concavity of zeros of bessel functions^†
• Asymptotic Formulas for Ultraspherical Polynomials P (λ) n (X) and their Zeros for Large Values of λ
• Inflection Points of Bessel Functions of Negative Order
• Inequalities and monotonicity properties for zeros of Hermite functions
• Inequalities for the Zeros of Ultraspherical Polynomials and Bessel Functions
• On the Derivative with Respect to a Parameter of a Zero of a Sturm–Liouville Function
• An inequality for Legendre polynomials
• Further results on McMahon's asymptotic approximations
• Error bounds for mcmahon's asympotic approximations of the zeros of the bessel functions
• Some Inequalities for the First Positive Zeros of Bessel Functions
• Bounds for Zeros of Some Special Functions
• Locating and computing in parallel all the simple roots of special functions using PVM