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
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Abstract | References | Similar Articles | Additional Information
Abstract: Freud and sub-range Freud polynomials are orthogonal with respect to the weight function ,
,
, supported on the whole real line
, resp. on strict subintervals thereof. The zeros of these polynomials are studied here as functions of
and shown, analytically and empirically by computation, to collectively increase or decrease on appropriate intervals of the variable
.
- [1] Walter Gautschi, Orthogonal Polynomials: Computation and Approximation, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2004. 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., Colloquium Publications, vol. XXIII, American Mathematical Society, Providence, R.I., 1975. MR 0372517
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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