On Some Properties of the Trigamma Function

Kwara Nantomah, Gregory Abe-I-Kpeng, Sunday Sandow

In 1974, Gautschi proved an intriguing inequality involving the gamma function $\Gamma$. Precisely, he proved that, for $z>0$, the harmonic mean of $\Gamma (z)$ and $\Gamma (1/z)$ can never be less…