Asymptotic expansions of the oblate spheroidal eigenvalues and wave functions for large parameter c

The asymptotic expansion of the oblate spheroidal eigenfunctions can be expanded in terms of the Laguerre functions of the first and second kinds, from which their asymptotic eigenvalue can be expressed in an inverse power series of c, where the parameter c is proportional to the operating frequency. Analytical expressions of the eigenvalue coefficients, as well as those of the expansion coefficients of the eigenfunctions, are derived and verified with numerical results.