Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

Monotonicity properties of the zeros of Freud and sub-range Freud polynomials: Analytic and empirical results


Author: Walter Gautschi
Journal: Math. Comp. 86 (2017), 855-864
MSC (2010): Primary 33C47, 33F05
DOI: https://doi.org/10.1090/mcom/3181
Published electronically: June 29, 2016
MathSciNet review: 3584551
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Freud and sub-range Freud polynomials are orthogonal with respect to the weight function $ w(t)=\vert t\vert^\mu \exp (-\vert t\vert^\nu )$, $ \mu >-1$, $ \nu >0$, supported on the whole real line $ \mathbb{R}$, resp. on strict subintervals thereof. The zeros of these polynomials are studied here as functions of $ \nu $ and shown, analytically and empirically by computation, to collectively increase or decrease on appropriate intervals of the variable $ \nu $.


References [Enhancements On Off] (What's this?)

  • [1] Walter Gautschi, Orthogonal polynomials: computation and approximation, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2004. Oxford Science Publications. MR 2061539
  • [2] W. Gautschi, Orthogonal polynomials in Matlab: Exercises and solutions, Software, Environments, Tools, SIAM, Philadelphia, PA, 2016.
  • [3] Gábor Szegő, Orthogonal polynomials, 4th ed., American Mathematical Society, Providence, R.I., 1975. American Mathematical Society, Colloquium Publications, Vol. XXIII. MR 0372517

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 33C47, 33F05

Retrieve articles in all journals with MSC (2010): 33C47, 33F05


Additional Information

Walter Gautschi
Affiliation: Department of Computer Science, Purdue University, West Lafayette, Indiana 47907-2066
Email: wgautschi@purdue.edu

DOI: https://doi.org/10.1090/mcom/3181
Keywords: Freud polynomials, sub-range Freud polynomials, zeros of orthogonal polynomials, Matlab software
Received by editor(s): September 8, 2015
Published electronically: June 29, 2016
Article copyright: © Copyright 2016 American Mathematical Society