On the concavity of zeros of bessel functions^†

Continuous ranking of zeros of special functions

“…The graphs in Fig. 1 complements those in [24, p. 510] where ±j νk is graphed against ν for k = 1, 2, 3, 4, and in [7] where j νκ is graphed against ν for various values of κ between 0 and 1. It is also worth mentioning that Olver [20] considered what amounts to j νκ for continuous κ while in [21], he considered it for continuous ν, both situations arising from a need to evaluate the zeros numerically.…”

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

“…or, in terms of our present notation, Now the first term on the right here is negative [1] and the sum of the two remaining terms will certainly be negative provided that (3.9) from (3.4) and (3.6) and this is certainly negative in case -0.8 < v < 0. Thus the second derivative of p 2 with respect to v is negative at points where the first derivative is 0; hence there can be only one such point and it is a relative maximum.…”

Monotonic sequences related to zeros of Bessel functions

“…we have g (ν) = dy ν1 /dν − π/4 which, in view of results in [4] decreases to the positive number 1−π/4, as ν → ∞. Thus g(ν) is increasing, g(− Watson [15, pp.…”