Digamma functional equation
From specialfunctionswiki
Theorem
The following formula holds: $$\psi(z)=\psi(z+1)-\dfrac{1}{z},$$ where $\psi$ denotes the digamma function.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.7 (8)$
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.3.5$
