On the zeros and turning points of special functions

Authors:
Javier Segura
Affiliations:
Depto. de Matemáticas, Universidad Carlos III de Madrid, 28911-Leganés, Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Year:
2003

Citing 4
Cited 3

Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros

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

Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
The Zeros of Special Functions from a Fixed Point Method

SIAM Journal on Numerical Analysis
A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions

Journal of Symbolic Computation - Special issue: Algebra and computer analysis

A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions

Journal of Symbolic Computation - Special issue: Algebra and computer analysis
New inequalities from classical sturm theorems

Journal of Approximation Theory
New inequalities from classical Sturm theorems

Journal of Approximation Theory

Quantified Score

Hi-index	0.01

Visualization

Abstract

Globally convergent fixed point iterations, together with bounds on differences of zeros from Sturm methods, are used to build efficient algorithms for the computation of the zeros of special functions satisfying first-order linear difference-differential equations. Bounds on the spacing between the zeros are obtained as a by-product. Turning points can also be computed in a similar way; new analytical information is also obtained in this case which, for instance, can be used to prove a conjecture by Elbert on the turning points of Bessel functions.