Transformation and summation formulae for Kampé de Fériet series

Euler’s two transformations are employed to establish several general transformation formulae for double hypergeometric series. These transformations yield further a number of reduction formulae for Kampé de Fériet series of types F 1 : 0 ; μ 1 : 1 ; λ , F 1 : 0 ; μ 0 : 2 ; λ and F 1 : 0 ; μ 2 : 0 ; λ . By specializing certain parameters, a list of new summation formulae for these Kampé de Fériet series are obtained.