Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among Whipple's identities include

(Bailey 1935, p. 15; Koepf 1998, p. 32), where  is a generalized hypergeometric function and  is a gamma function, and

(Bailey 1935, p. 28).

REFERENCES:

Bailey, W. N. "Whipple's Theorem on the Sum of a ." §3.4 in Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 16, 1935.

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, 1998.

Whipple, F. J. W. "Well-Poised Series and Other Generalized Hypergeometric Series." Proc. London Math. Soc. Ser. 2 25, 525-544, 1926.