We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ frac{Gamma(lambda)}{Gamma( u)} sum^{infty}_{n=1}{frac{Gamma( u+n)}{nGamma(lambda+n)}_{p+2}F_{p+1}(a_1, cdots, a_{p+1},lambda + n; x/a)} = sum^{infty}_{k=0}{frac{(a_1)_k cdots (a_{(p+1)}{(b_1)_k cdots (b_p)_k K!} (frac{x}{a})^k [psi(lambda + k) - psi(lambda - u + k)]}, Re(lambda) > Re( u) geq 0 $$ and explain some special cases.