1. For Hermite polynomial we use the (standard) definition given for instance inHigher Transcendental Functions, edited byA. Erdélyi, Vol.2 (New York, N. Y., 1953).
2. G. Szegö:Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ.,23, 1939, subsect.6·7.
3. F. Calogero:Journ. Math. Phys.,12, 419 (1971).
4. M. Adler:A new integrable system and a confecture by Calogero, NYU preprint, unpublished (1975);
5. Some finite-dimensional integrable systems, inProceedings of the NSF Conference on Solitions, Tucson, January 1976, edited byH. Flaschka andD. W. McLaughlin (to appear in theRocky Mountain Mathematics, Journal, 1977).