Fig. 2
From: Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions
The exact numerical solution of the first (\(n = 1\)) zero \(\lambda _{1,\nu }\), exemplary for \(\nu = 2\) [black solid line obtained from Eq. (40)] in comparison with approximate solutions (red solid line obtained from Eq. (51) and blue solid line obtained from Eq. (53) for small values of the index \(\nu \)) and results from Grebenkov [green solid line obtained from Eq. (55)], Gottlieb [green dashed line obtained from Eq. (54)], and Buchholz [green dotted line obtained from Eq. (56)].