HypExplicit[exp, nu] expresses Hypergeometric functions in exp by their definition in terms of a sum (the Sum is omitted and nu is the summation index).
Hypergeometric2F1[a, b, c, z]
HypExplicit[%, \[Nu]]\, _2F_1(a,b;c;z)
\frac{\Gamma (c) z^{\nu } \Gamma (a+\nu ) \Gamma (b+\nu )}{\Gamma (a) \Gamma (b) \Gamma (\nu +1) \Gamma (c+\nu )}
HypergeometricPFQ[{a, b, c}, {d, e}, z]
HypExplicit[%, \[Nu]]\, _3F_2(a,b,c;d,e;z)
\frac{\Gamma (d) \Gamma (e) z^{\nu } \Gamma (a+\nu ) \Gamma (b+\nu ) \Gamma (c+\nu )}{\Gamma (a) \Gamma (b) \Gamma (c) \Gamma (\nu +1) \Gamma (d+\nu ) \Gamma (e+\nu )}