Certain bilateral generating relations for generalized hypergeometric functions (Q1917767)

In this short note the authors have given bilateral generating relations (in the form of a single result) for the generalized hypergeometric functions \(I^{\alpha; (a_p)}_{n; (b_q)} (x,w)\), defined by \[ I^{\alpha; (a_p)}_{n; (b_q)} (x,w) = {1 \over n! (x - w)^{[\alpha_w]}} \Delta^n_{x,w} \left[ (x - w)^{\bigl[ (\alpha + n) w \bigr]} _{p + 1} F_q \left( (a_p), - {x \over w}; (b_q); w \right) \right] \] where, \[ \Delta_{x,w} f(x) = {f(x + w) - f(x) \over w}. \] To establish their result they used series manipulation technique. The result involves generalized Lauricella hypergeometric functions of four variables and is too lengthy to be reproduced here.