Common zeros of two Bessel functions. II. Approximations and tables

Abstract:

In [1] it was shown that two Bessel functions ${J_\nu }(x)$, ${J_\mu }(x)$ could have two zeros which were common to both functions, and a computer program was made which takes approximate values of $\nu$, $\mu$ and ${j_{\nu ,k}} = {j_{\mu ,h}}$ and ${j_{\nu , k + n}} = {j_{\mu ,h + m}}$ and from them computes the exact values. Here it will be shown how to find the necessary approximate values to initiate the computation. A table of the smaller ratios m : n with the orders of the functions less than one hundred is given.