Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series
This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of -orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when . The underlying algebraic framework allowed a systematic derivation...
The Hille-Hardy formula is a bilinear generating function, involving products of Laguerre polynomials. We use the point of view, developed in previous publications, to propose an operational method which allows a fairly direct derivation of this kind of formulae.