On inflection points of Bessel functions of the second kind of positive order

ABSTRACTIn this paper, we study inflection points of Bessel functions of the second kind Yν(x) of positive order. In particular, we prove that there exists a positive number ν∗>0 such that for all ν>ν∗ at least two positive inflection points reside before the first positive zero yν of Yν. As a consequence, we prove that the function ν↦yν″, where yν″ is the smallest positive inflection point of Yν, is discontinuous on (0,∞). We present lower and upper bounds for these inflection points and formulate some conjectures.