1. Throughout this paper we use the definitions of special functions given inHigher Transcendental Functions, edited byA. Erdélyi, Vol.2 (New York, N. Y., 1953).
2. For a survey of these problems seeF. Calogero:Integrable many-body problems, inNonlinear Equations in Physics and Mathematics, edited byA. O. Barut,Proceedings of an Advanced Study Institute, Istanbul, August 1977 (Reidel, and New York, N. Y., 1978).
3. A prime appended to a sum (product) indicates hereafter that the singular (vanishing) term is omitted.
4. See, for instance,M. Abramowitz andA. Stegun:Handbook of Mathematical Functions, Chapt. 23 (New York, N. Y., 1965).
5. A prime appended to a function indicates hereafter differentiation.