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
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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