A Note on the Rayleigh Polynomials

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1978 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 9, pages 825-834 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Obi, E. C.;

doi: 10.1137/0509064

A Note on the Rayleigh Polynomials

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Abstract

Some formulae and representations of the nth order Rayleigh functions, $\sigma _n $, and their associated polynomials, $\phi _n $, are used to determine polynomials which dominate, or are dominated by, $\phi _n $, and to discuss improved lower bounds for their real roots. In the process the ties between $\phi _n $, and the Catalan numbers are enhanced.

Keywords

Rayleigh Polynomials, Bessel and Airy functions, cylinder functions, ${}_0F_1$, Other special functions, Rayleigh Function

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