Integral representation and generating functions for the polynomialsU _n ^(α,β) (x)

F. Calogero:Singular integral operators with integral eigenvalues and polynomial eigenfunctions, in press toNuovo Cimento, B.Google Scholar

For the definition of Tchebichef polynomials see any standard compilation, f.i.:A. Erdélyi (editors):Higher Trascendental Functions, Vol.2 (New York, N. Y., 1953);M. Abramowits andI. A. Stegun (Editors):Handbook of Mathematical Functions (New York, N. Y., 1955);I. S. Gradshteyn andI. M. Ryzhik:Tables of Integrals, Series and Products (New York, N. Y., 1965) (translation from Russian edited byA. Jeffrey).Google Scholar

See, for instance, eqs. 15.2(19) and 15.2(25) inTables of Integral Transforms, edited byA. Erdélyi, Vol.2 (New York, N. Y., 1954).Google Scholar