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On the Points of Inflection of Bessel Functions of Positive Order, II

Published online by Cambridge University Press:  20 November 2018

R. Wong  and
T. Lang
R. Wong
Affiliation:
Department of Applied Mathematics, University of Manitoba, WinnipegManitoba R3T2N2.
T. Lang
Affiliation:
Department of Applied Mathematics, University of Manitoba, WinnipegManitoba R3T2N2.
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Let jν, 1, jν,2, … denote the positive zeros of the Bessel function Jν(x), and similarly, let j'v,1, j'v,2, … denote the positive zeros of J'v(x), which are the positive critical points of Jv(x). It is well-known that when v is positive, both jν ,k. it and j'ν k are increasing functions of ν; see, e.g., [12, pp. 246 and 248]. Recently, Lorch and Szego [6] have attempted to show that the same is true for the positive zeros j″v,1, j″v,2, … of j″v(x), which are the positive inflection points of Jv(x).

Keywords

33A4041A60Inflection pointBessel functionintegral transformuniform asymptotic expansionAiry function
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 628 - 651
Copyright
Copyright © Canadian Mathematical Society 1991

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