Digamma at 1/2

Theorem

The following formula holds: $$\psi \left( \dfrac{1}{2} \right) = -\gamma - 2 \log(2),$$ where $\psi$ denotes the digamma function, $\gamma$ denotes the Euler-Mascheroni constant, and $\log$ denotes the logarithm.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.3.3$