Generating relations of the hypergeometric functions by the Lie group-theoretic method (Q1595884)

The generating relations for a set of hypergeometric functions defined by \[ \psi_{\alpha,\beta,\nu,m}(x)= {\beta^m(\nu)_m\over m!} (1- x)^{-m/2}{_2F_1}(- m,\alpha;\nu; x/\beta) \] are obtained by using the representation of the Lie group \(\text{SL}(2,\mathbb{C})\) giving a suitable interpretation to the index \(m\) in order to derive the elements of Lie algebra. Several results involving classical polynomials, namely the Laguerre, Hermite, Meixner, Gottlieb and Krawtchouk polynomials are derived as special cases of the main results.