Inequalities for the zeros of Bessel functions. (English) Zbl 0548.33004

McCann, Roger C.

Dynamical systems, Proc. int. Symp., Gainesville/Fla. 1976, 465-466 (1977).

[For the entire collection see Zbl 0532.00013.]
This paper contains a summary of the author’s proof that \(j_{pn}/p\) decreases as p increases, \(0<p<\infty\) where \(j_{pn}\) is the nth positive x-zero of \(J_ p(x)\). More details are given in the author’s paper in SIAM J. Math. Anal. 8, 166-170 (1977; Zbl 0342.33021).

Reviewer: M.E.Muldoon

MSC:

33C10

Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Keywords:

Bessel functions; zeros; inequalities; monotonicity

Citations:

Zbl 0532.00013; Zbl 0342.33021