A Unimodal Property of Purely Imaginary Zeros of Bessel and Related Functions
Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 365-373

Voir la notice de l'article provenant de la source Cambridge University Press

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 .
DOI : 10.4153/CMB-1994-054-3
Mots-clés : 33A40
Kokologiannaki, C. G.; Muldoon, M. E. A Unimodal Property of Purely Imaginary Zeros of Bessel and Related Functions. Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 365-373. doi: 10.4153/CMB-1994-054-3
@article{10_4153_CMB_1994_054_3,
     author = {Kokologiannaki, C. G. and Muldoon, M. E.},
     title = {A {Unimodal} {Property} of {Purely} {Imaginary} {Zeros} of {Bessel} and {Related} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {365--373},
     year = {1994},
     volume = {37},
     number = {3},
     doi = {10.4153/CMB-1994-054-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-054-3/}
}
TY  - JOUR
AU  - Kokologiannaki, C. G.
AU  - Muldoon, M. E.
TI  - A Unimodal Property of Purely Imaginary Zeros of Bessel and Related Functions
JO  - Canadian mathematical bulletin
PY  - 1994
SP  - 365
EP  - 373
VL  - 37
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-054-3/
DO  - 10.4153/CMB-1994-054-3
ID  - 10_4153_CMB_1994_054_3
ER  - 
%0 Journal Article
%A Kokologiannaki, C. G.
%A Muldoon, M. E.
%T A Unimodal Property of Purely Imaginary Zeros of Bessel and Related Functions
%J Canadian mathematical bulletin
%D 1994
%P 365-373
%V 37
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-054-3/
%R 10.4153/CMB-1994-054-3
%F 10_4153_CMB_1994_054_3

[1] 1. Elbert, Á., Concavity of the zeros of Bessel functions, Studia Sci. Math. Hungar. 12(1977), 81–88. Google Scholar

[2] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 13. Mercer, A. McD., The zeros of as a function of order, Internat. J. Math. Math. Sci. 15(1992), 319–322. Google Scholar

[14] 14. Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd éd., Cambridge University Press, 1944. Google Scholar

[15] 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

Cité par Sources :