Roots of two transcendental equations involving spherical Bessel functions

Abstract:

Roots of the transcendental equations ${j_l}(\alpha \lambda ){y_l}(\lambda ) = {j_l}(\lambda ){y_l}(\alpha \lambda )$ and \[ {[x{j_l}(x)]’_{x = \alpha \eta }}{[x{y_l}(x)]’_{x = \eta }} = {[x{j_l}(x)]’_{x = \eta }}{[x{y_l}(x)]’_{x = \alpha \eta }}\] for the spherical Bessel functions of the first and second kind, ${j_l}(z)$ and ${y_l}(z)$, have been computed. The ranges for the parameter $\alpha$, the order l and the root index n are: $\alpha = 0.1(0.1)0.7$, $l = 1(1)15$, $n = 1(1)30$.