Geodesic
On the Points of Inflection of Bessel Functions of Positive Order, II
Canadian journal of mathematics, Tome 43 (1991) no. 3, pp. 628-651

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

Let j ν, 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).
DOI : 10.4153/CJM-1991-037-4
Mots-clés : 33A40, 41A60, Inflection point, Bessel function, integral transform, uniform asymptotic expansion, Airy function 
Wong, R.; Lang, T. On the Points of Inflection of Bessel Functions of Positive Order, II. Canadian journal of mathematics, Tome 43 (1991) no. 3, pp. 628-651. doi: 10.4153/CJM-1991-037-4
@article{10_4153_CJM_1991_037_4,
     author = {Wong, R. and Lang, T.},
     title = {On the {Points} of {Inflection} of {Bessel} {Functions} of {Positive} {Order,} {II}},
     journal = {Canadian journal of mathematics},
     pages = {628--651},
     year = {1991},
     volume = {43},
     number = {3},
     doi = {10.4153/CJM-1991-037-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-037-4/}
}
TY  - JOUR
AU  - Wong, R.
AU  - Lang, T.
TI  - On the Points of Inflection of Bessel Functions of Positive Order, II
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 628
EP  - 651
VL  - 43
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-037-4/
DO  - 10.4153/CJM-1991-037-4
ID  - 10_4153_CJM_1991_037_4
ER  - 
%0 Journal Article
%A Wong, R.
%A Lang, T.
%T On the Points of Inflection of Bessel Functions of Positive Order, II
%J Canadian journal of mathematics
%D 1991
%P 628-651
%V 43
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-037-4/
%R 10.4153/CJM-1991-037-4
%F 10_4153_CJM_1991_037_4

[1] 1. Abramowitz, M. and Stegun, I., Handbook of mathematical functions, N.B.S. Applied Math. Ser. 55 (Washington, D. C, 1964). Google Scholar

[2] 2. Gatteschi, L., Limitazione degli errori nelleformule asintoticheper le funzioni speciali, Rend. Semin. Mat. Univ. e Pol, Torino 16 (1956-1957., 83–97. Google Scholar

[3] 3. Hethcote, H.W., Error bounds for asymptotic approximations of zeros of transcendental functions, SIAM J. Math. Anal., 1 (1970), 147–152. Google Scholar

[4] 4. Hethcote, H.W., Bounds for zeros of some special functions, Proc. Amer. Math. Soc, 25 (1970), 12–1.A. Google Scholar

[5] 5. Lang, T., Asymptotic analysis of the inflection points of the Bessel function Jv(x), M.Sc. Thesis, University of Manitoba, 1989. Google Scholar

[6] 6. Lorch, L. and Szego, P., On the points of inflection of Bessel functions of positive order, . ., Can. J. Math., 42 (1990), 933–948. Google Scholar

[7] 7. O.I. Marichev, Handbookof integral transforms of higher transcendental functions, theory and algorithmic tables (Ellis Horwood Ltd., West Sussex, England, 1983). Google Scholar

[8] 8. Olver, F.W.J., The asymptotic expansion of Bessel functions of large order, Philos. Trans. Roy. Soc. London Ser. A, 247 (1954), 328–368. Google Scholar

[9] 9. Olver, F.W.J., Tables of Bessel functions of moderate or large orders, Math. Tables Nat. Phys. Lab., Vol. 6 (Her Majesty's Stationery Office, London, 1962). Google Scholar

[10] 10. Olver, F.W.J., Error bounds for first approximations in turning point problems, J. Soc. Indust. Appl. Math., 11 (1963), 748–772. Google Scholar

[11] 11. Olver, F.W.J., Error bounds for asymptotic expansions in turning point problems, J. Soc. Indust. Appl. Math., 12 (1964), 200–214. Google Scholar

[12] 12. Olver, F.W.J., Asymptotics and special functions (Academic Press, New York, 1974). Google Scholar

[13] 13. Watson, G.N., Theory of Bessel functions (Cambridge University Press, Cambridge, 1944). Google Scholar

[14] 14. Wong, R., Explicit error terms for asymptotic expansions ofMellin convolutions, J. Math. Anal. Appl., 72 (1979), 740–756. Google Scholar

[15] 15. Wong, R., Error bounds for asymptotic expansions of integrals, SIAM Rev., 22 (1980), 401–435. Google Scholar

[16] 16. Wong, R., Applications of some recent results in asymptotic expansions, Proc. 12th Winnipeg Conf. on Numerical Methods of Computing, Congress Numer., 37(1983), 145–182. Google Scholar

Cité par Sources :