Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-29T00:15:35.776Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 November 2018

Lee Lorch  and
Peter Szego
Lee Lorch
Affiliation:
York University, North York, OntarioM3J 1P3
Peter Szego
Affiliation:
75 Glen Eyrie Avenue, San Jose California 95125, U. S. A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The primary concern addressed here is the variation with respect to the order v > 0 of the zeros jʺvk of fixed rank of the second derivative of the Bessel function Jv(x) of the first kind. It is shown that jʺv1 increases 0 < v < ∞ (Theorem 4.1) and that jʺvk increases in 0 < v ≤ 3838 for fixed k = 2, 3,… (Theorem 10.1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 5 , 01 October 1990 , pp. 933 - 948
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Butlewski, Z., Sur les intégrales d'une équation différentielle du second ordre Mathematica (Cluj) 12 (1936) 36–48.Google Scholar
2. Elbert, Árpád and Laforgia, Andrea, On the zeros of derivatives of Bessel functions J. Appl. Math. and Physics (ZAMP) 34 (1983) 774–786.Google Scholar
3. Erdelyi, A. et al, Higher transcendental functions Vol. II, McGraw-Hill Book Co., New York Toronto London, 1953.Google Scholar
4. Gatteschi, Luigi and Laforgia, Andrea, Nuove disuguaglianze per il primo zero ed il primo massimodella funzione di Bessel Jv (x) Rend. Sem. Mat. Univers. Politecn. Torino 34 (1975–76. 441–24.Google Scholar
5. Lorch, Lee, Muldoon, Martin and Szego, Peter, Higher monotonicity properties of Sturm-Liouville funcitons IV Canadian J. Math. 24 (1972) 349–368.Google Scholar
6. Lorch, Lee, Muldoon, Martin and Szego, Peter, On the points of inflection of Bessel functions ofnegative order. Google Scholar
7. Olver, F.W.J., Asymptotics and special functions Academic Press. New York and London, (1974).Google Scholar
8. Schafheitlin, Paul, Über der Verlauf der Besselschen Funktionen zweiter Art Jahresb. d. Deutsche Math. Verein. 16 (1907) 272–279.Google Scholar
9. Szegö, Gabor, Orthogonal polynomials 4th éd., Colloquium Publ. Amer. Math. Soc, 23 (1975) Amer. Math. Soc, Providence, R. I.Google Scholar
10. Vosmanský, J., Certain higher monotonicity properties of Bessel functions Archivum Math. (Brno) 13 (1977)55–64.Google Scholar
11. Watson, G.N. A treatise on the theory of Bessel functions 2nd. ed. Cambridge University Press, Cambridge 1944.Google Scholar
12. Wong, Roderick and Lang, T., On the points of inflection of Bessel functions of positive order II, Canadian J. Math, (to appear).Google Scholar

A correction has been issued for this article:

Corrigenda