Whipple's Transformation

${}_7F_6 \left[{\matrix{a, 1+{\textstyle{1\over 2}}a, b, c, d, e, -m\cr {\textstyle{1\over 2}}a,1+a-b,1+a-c,\cr \hfil 1+a-d,1+a-e,1+a+m\cr}}\right]$
$={(1+a)_m(1+a-d-e)_m\over (1+a-d)_m(1+a-e)_m} {}_4F_3\left[{\matrix{1+a-b-c, d, e, -m\cr 1+a-b, 1+a-c, d+e-a-m\cr}}\right],$

where ${}_7F_6$ and ${}_4F_3$ are Generalized Hypergeometric Functions and $\Gamma(z)$ is the Gamma Function.

See also Generalized Hypergeometric Function