We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained.
Miller, A. R., & Paris, R. B. (2012). Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x). Integral Transforms and Special Functions, 23(1), 21-33. https://doi.org/10.1080/10652469.2011.552263