Ordering relations between the zeros of miscellaneous bessel functions

Abstract

A method applied in previous work [l,10,11] to the study of the zeros of the ordinary Bessel function J_ε (z) is here extended and also applied to the zeros of the function , is the derivative of J_ν (z). It is proved that in the case where ν is real and ν>−1, the zeros of F ν(z) are the same with the zeros of the function , where T (x), in the case of real positive zeros, meromorphic with poles the positive zeros of J_ν(z). Moreover the function T(x) is real for x real and increases as x increases in each of the intervals . This result unifies generalizes and improves, many known results for the zeros of the interesting function .

AMS (MOS):

• 33A40
• 47B05