Transformations of Kummer-type for 2F2-series and their q-analogues

Linearization method and series rearrangement are employed to review the transformations of Kummer-type for the generalized hypergeometric F 2 2 -series due to Exton [On the reducibility of the Kampé de Fériet function, J. Comput. Appl. Math. 83 (1997) 119], Miller [On a Kummer-type transformation for the generalized hypergeometric function F 2 2 , J. Comput. Appl. Math. 157 (2003) 507] and Paris [A Kummer-type transformation for a F 2 2 hypergeometric function, J. Comput. Appl. Math. 173 (2005) 379]. Several new transformation formulae as well as their q -analogues for the same F 2 2 -series are also established.