FURTHER RESULTS ON THE ZEROS OF BESSEL FUNCTIONS
Let c^^ be the k th positive zero of the cylinder function C^(x) = J^(x) cos α Y v(x) sin a , 0 .< α < π , where J v(x) and Y v(x) are the Bessel functions of the first and second kind, respectively. We give a lower bound for the second derivative of c ^ with respect to ν and we prove that the third derivative of c ^ is positive for ν 5. 0 and k — — > 0.7070. As a consequence of this property a new inequality for c v k is proved. AMS Classification: Primary 33 A 40