Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T18:11:45.585Z Has data issue: false hasContentIssue false
  • English
  • Français

A Unimodal Property of Purely Imaginary Zeros of Bessel and Related Functions

Published online by Cambridge University Press:  20 November 2018

C. G. Kokologiannaki ,
M. E. Muldoon  and
P. D. Siafarikas
C. G. Kokologiannaki
Affiliation:
Department of Mathematics, University of Patras, 261 10 Patras, Greece
M. E. Muldoon
Affiliation:
Department of Mathematics and Statistics, York University, North York, Ontario, M3J 1P3
Rights & Permissions [Opens in a new window]

Abstract

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.

We show, among other things, that, for n = 0,1, the negative of the square of a purely imaginary zero of is unimodal on (n — 2, n — 1). One of the important tools in the proof is the Mittag-Leffler partial fractions expansion of .

Keywords

33A40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 365 - 373
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Elbert, Á., Concavity of the zeros of Bessel functions, Studia Sci. Math. Hungar. 12(1977), 81–88.Google Scholar
2. Elbert, Á. and Laforgia, A., On the square of the zeros of Bessel functions, SIAM J. Math. Anal. 15(1984), 206–212.Google Scholar
3. Ifantis, E. K., Siafarikas, R D. and Kouris, C. B., The imaginary zeros of a mixed Bessel function, Z. Angew. Math. Phys. 39(1988), 157–165.Google Scholar
4. Ifantis, E. K. and Siafarikas, P. D., A result on the imaginary zeros of , J. Approx. Theory 62(1990), 192–196.Google Scholar
5. Ismail, M. E. H. and Muldoon, M. E., On the variation with respect to a parameter of zeros of Bessel and q-Bessel functions, J. Math. Anal. Appl. 135(1988), 187–207.Google Scholar
6. Ismail, M. E. H. and Muldoon, M. E., Zeros of combinations of Bessel functions and their derivatives, Appl. Anal. 31(1988), 72–90.Google Scholar
7. Ismail, M. E. H. and Muldoon, M. E., Bounds for the small real and purely imaginary zeros of Bessel and related functions, Meth. Appl. Anal., to appear.Google Scholar
8. Kerimov, M. K. and Skorokhodov, S. L., Evaluation of complex zeros of Bessel functions Ju(z) and Iv(z) and their derivatives, Comput. Math. Math. Phys. 24(1984), 131–141; Russian original, Zh. Vychisl. Mat. i Mat. Fiz. 24(1984), 1497–1513.Google Scholar
9. Kerimov, M. K. and Skorokhodov, S. L., Calculation of the multiple zeros of the derivatives of cylindrical Bessel functions Jv(z) and Yu(z), Comput. Math. Math. Phys. 25(1985), 101–107; Russian original, Zh. Vychisl. Mat. i Mat. Fiz. 25(1985), 1749–1760.Google Scholar
10. Kokologiannaki, C. G. and Siafarikas, P. D., An alternative proof of the monotonicity of ju\”, Boll. Un. Mat. Ital. (7-A) 7(1993), 373–376.Google Scholar
11. Laforgia, A. and Muldoon, M. E., Monotonicity and concavity properties of zeros of Bessel functions, J. Math. Anal. Appl. 98(1984), 470–477.Google Scholar
12. Lorch, L. and Szego, P., On the points of inflection of Bessel functions of positive order, Canad. J. Math. 42(1990), 933–948; ibid, 1132.Google Scholar
13. Mercer, A. McD., The zeros of as a function of order, Internat. J. Math. Math. Sci. 15(1992), 319–322.Google Scholar
14. Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd éd., Cambridge University Press, 1944.Google Scholar
15. Wong, R. and Lang, T., On the points of inflection of Bessel functions of positive order, II, Canad. J. Math. 43(1991), 628–651.Google Scholar