The Turning Point of Bessel Functions and Applications to the Electronic Eigenvalues in Wedge-Shaped Films
01 Jul 1993-Physica Status Solidi B-basic Solid State Physics (John Wiley & Sons, Ltd)-Vol. 178, Iss: 1
About: This article is published in Physica Status Solidi B-basic Solid State Physics.The article was published on 1993-07-01. It has received 1 citations till now. The article focuses on the topics: Struve function & Cylindrical harmonics.
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28 Dec 1954-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, new series for the zeros and associated values are derived by reversion and used to determine the distribution of zeros of functions of large order in the z-plane.
Abstract: New expansions are obtained for the functions Iv{yz), ) and their derivatives in terms of elementary functions, and for the functions J v(vz), Yv{vz), H fvz) and their derivatives in terms of Airy functions, which are uniformly valid with respect to z when | | is large. New series for the zeros and associated values are derived by reversion and used to determine the distribution of the zeros of functions of large order in the z-plane. Particular attention is paid to the complex zeros of 7„(z) and the Hankel functions when the order n is an integer or half an odd integer, and for this purpose some new asymptotic expansions of the Airy functions are derived. Tables are given of complex zeros of Airy functions and other quantities which facilitate the rapid calculation of the smaller complex zeros of 7„(z), 79(z), and the Hankel functions and their derivatives, when 2 n is an integer, to an accuracy of three or four significant figures.
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TL;DR: Two algorithms are presented for finding a zero of a real continuous function defined on a given interval using mixtures of linear interpolation, rational interpolations, and bisectmn.
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