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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Monotonicity properties of the zeros of Freud and sub-range Freud polynomials: Analytic and empirical results
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by Walter Gautschi PDF
Math. Comp. 86 (2017), 855-864 Request permission

Abstract:

Freud and sub-range Freud polynomials are orthogonal with respect to the weight function $w(t)=|t|^\mu \exp (-|t|^\nu )$, $\mu >-1$, $\nu >0$, 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
  • Walter Gautschi, Orthogonal polynomials: computation and approximation, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2004. Oxford Science Publications. MR 2061539
  • W. Gautschi, Orthogonal polynomials in Matlab: Exercises and solutions, Software, Environments, Tools, SIAM, Philadelphia, PA, 2016.
  • Gábor Szegő, Orthogonal polynomials, 4th ed., American Mathematical Society 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
  • MR Author ID: 71975
  • Email: wgautschi@purdue.edu
  • Received by editor(s): September 8, 2015
  • Published electronically: June 29, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 855-864
  • MSC (2010): Primary 33C47, 33F05
  • DOI: https://doi.org/10.1090/mcom/3181
  • MathSciNet review: 3584551