Methods of Computation

An effective way of computing Γ ( z ) in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion Or we can use forward recurrence, with an initial value . For the left half-plane we can continue the backward recurrence or make use of the reflection formula .

Similarly for ln Γ ( z ) , ψ ( z ) , and the polygamma functions.

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