(Bailey 1935, p. 25), where  and  are generalized hypergeometric functions with argument  and  is the gamma function.

Another transformation due to Whipple (1926ab) is given by

for one of  and  a nonnegative integer (Andrews and Burge 1993).

REFERENCES:

Andrews, G. E. and Burge, W. H. "Determinant Identities." Pacific J. Math. 158, 1-14, 1993.

Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 25 and 29, 1935.

Whipple, F. J. W. "On Well-Poised Series, Generalized Hypergeometric Series Having Parameters in Pairs, Each Pair with the Same Sum." Proc. London Math. Soc. 24, 247-263, 1926a.

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

Whipple, F. J. W. "A Fundamental Relation Between Generalized Hypergeometric Series." Proc. London Math. Soc. 26, 257-272, 1927.