In a recent paper (Proc. Roy. Soc. Edin., vol. lix, 1939, pp. 49–54) expressions in multiple series with argument 1 – z were found for Generalised Hypergeometric Functions of the type

where p > 1. These formulæ are generalisations of known formulæ for the ordinary hypergeometric function F(α, β; ρ; z), and they are established by induction. The same method will be here employed to obtain generalisations of other known formulæ, these generalisations being in the form of multiple series.