Monotonic sequences related to zeros of Bessel functions

被引：0

作者：

Lee Lorch

Martin E. Muldoon

机构：

[1] York University,Department of Mathematics & Statistics

来源：

Numerical Algorithms | 2008年 / 49卷

关键词：

Bessel functions; Cylinder functions; Inequalities; Monotonicity properties; Primary 33C10; Secondary 34C10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In the course of their work on Salem numbers and uniform distribution modulo 1, A. Akiyama and Y. Tanigawa proved some inequalities concerning the values of the Bessel function J0 at multiples of π, i.e., at the zeros of J1/2. This raises the question of inequalities and monotonicity properties for the sequences of values of one cylinder function at the zeros of another such function. Here we derive such results by differential equations methods.

引用

页码：221 / 233

页数：12

共 18 条

[1] Akiyama S.(2004)Salem numbers and uniform distribution modulo 1 Publ. Math. (Debr.) 64 329-341
[2] Tanigawa Y.(1991)An approximation for the zeros of Bessel functions Numer. Math. 59 647-657
[3] Elbert .̇(2001)Some recent results on the zeros of Bessel functions and orthogonal polynomials. Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications (Patras, 1999) J. Comput. Appl. Math. 133 65-83
[4] Elbert Á.(1983)On the concavity of zeros of Bessel functions Appl. Anal. 16 261-278
[5] Elbert Á.(1984)On the square of the zeros of Bessel functions SIAM J. Math. Anal. 15 206-212
[6] Gatteschi L.(1986)Monotonicity properties of the zeros of Bessel functions SIAM J. Math. Anal. 17 1483-1488
[7] Laforgia A.(2000)Further results on McMahon’s asymptotic approximations J. Phys. A: Math. Gen. 33 6333-6341
[8] Elbert Á.(1950)Valutazione dell’errore nella formula di McMahon per gli zeri della Rivista Mat. Univ. Parma 1 347-362
[9] Laforgia A.(2002)( J. Comput. Appl. Math. 144 7-27
[10] Elbert Á.(1980)) di Bessel nel caso 0 ≤ Calcolo 17 211-220

← 1 2 →