Triple Gaussian hypergeometric functions. II (Q1901620)

The author had investigated possible equivalences of systems of partial differential equations associated with hypergeometric functions \(F_G\) and \(F_T\) of three variables of second order introduced by \textit{G. Lauricella} [Rend. Circ. Mat. Palermo 7, 111-158 (1893)] and \textit{S. Saran} [Ganita 5, No. 2, 77-91 (1954; Zbl 0058.00296), Corrigendum. ibid. 7, 65 (1956)] in [Part I: Indian J. Pure Appl. Math. 25, No. 10, 1073-1079 (1994; Zbl 0824.33007)] which reduce to forms of Gauss' hypergeometric function \(_2F_1\) when any two of the variables are suppressed. In this paper, the triple hypergeometric functions \(F_A^{(3)}\), \(F_E\), \(F_N\) and \(F_F\), occurring in triple Gaussian hypergeometric functions listed by H. M. Srivastava and P. W. Karlsson [Multiple Gaussian hypergeometric series (1985; Zbl 0552.33001)] are similarly treated and it is shown that the different partial differential systems associated with these functions are mutually equivalent.