Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Some new asymptotic expansions for Bessel functions of large orders

F. W. J. Olvera1

a1 National Physical Laboratory Teddington, Middlesex

During the course of recent work (6) on the zeros of the Bessel functions Jn(x) and Yn(x), it became evident that the theory of the asymptotic expansion of Bessel functions whose arguments and orders are of comparable magnitudes was incomplete. The existing expansions for large orders are those of Debye and Meissel, detailed derivations of both of which are given by Watson ((8), pp. 237–48).

(Received July 13 1951)