DLMF: GA.21 Methods of Computation

§GA.21. Methods of Computation

An effective way of computing $\Gamma\!\left(z\right)$ in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion (GA.11.3). Or we can use forward recurrence, with an initial value obtained e.g. from (GA.7.3). For the left half-plane we can continue the backward recurrence or make use of the reflection formula (GA.5.3).

Similarly for $\mathrm{ln}\Gamma\!\left(z\right)$ , $\psi\!\left(z\right)$ , and the polygamma functions.

For a comprehensive survey see van der Laan and Temme(1984)(Chapter III). See also Borwein and Zucker(1992).