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An identity, relating a certain infinite continued fraction to the ratio of two contiguous Bessel functions, is exploited to derive the representation of a single Bessel function in terms of a series of products of continued fractions. This representation is made the basis of a new method for computing numerically Bessel functions of the first kind. The method is seen to be especially valuable in computing Bessel functions of order much larger tan unity.

A formalism is developed, employing an improved semi-classical theory of electrodynamics, with which it is possible to treat interacting systems of radiation and large or small numbers of atoms. The theory differs from the ordinary semiclassical theory as it is most commonly employed in two ways: (1) the neoclassical theory takes consistent account of the effect of the atoms on the electromagnetic fields, as well as the effect of the fields on the atoms; (2) the neoclassical theory avoids the use of perturbation theory in the usual sense, and does not introduce the concept of transition probability. The neoclassical theory is based on the attempt to integrate Schrodinger's equation directly. (Author)