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)
.