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But not only two of them. There are much more factorial generalizations which interpolate integer factorials. End even have not poles! For example the Hadamard generalization of factorials, look on Wolfram.
In fact |Γ(s)Γ(2−s)|=|Γ(s)Γ(s−1)Γ(2−s)Γ(s−1)|=1π|sinπs||Γ(s)||Γ(s−1)|. Due to the well-known inequality |Γ(x+iy)|≤|Γ(x)| both gammas are ≤1. But why sinus is power-bounded?
I did not find anything about 1F2 in the cited paper of Whipple. It seems there are no such factorization via more simple hypergeometric functions at least for general parameters. Otherwise a problem of asymptotics of 1F2 zeroes would be reduced somehow to something reasonable. But this is unsolved problem as far as I know.