Another new hypergeometric generating relation contiguous to that of Exton (Q2764924)

By standard series manipulations and a reducible case of \(_2F_1\) the authors arrive at the generating function relation NEWLINE\[NEWLINE\sum^\infty_{n=0} {(d)_n \Bigl(d+ {1\over 2}\Bigr)_n x^{2n} \over \Bigl({3\over 2}\Bigr)_n n!}F \left[ \begin{matrix} -n,-n-{1\over 2},& (a);\\ & (h); \end{matrix} y\right] ={1\over 2x (1-2d)} \bigl[f(x,y)- f(-x,y)\bigr],NEWLINE\]NEWLINE NEWLINE\[NEWLINEf(x,y)=(1+x)^{1-2d} F\left[\begin{matrix} (a), d,d & -{1\over 2};\\ & (h); \end{matrix}{x^2y \over(1+x)^2} \right].NEWLINE\]NEWLINE Here, \(F\) is a generalized hypergeometric function and \((a)\), \((h)\) are sets of parameters. Some particular cases are discussed.