Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

Appendix F 288
Appendix F: The Gamma function Γ (x)
• If is a positive integer, the Gamma function is
Γ () =( − 1)!
(F.1)
• The Gamma function smoothly interpolates between all points ( ) given by
=( − 1)! for positive non-integer (cf. Fig. F.1).
• The Gamma function is defined for all complex numbers with a positive real
part as
Z ∞
Γ () = −1 −
(F.2)
0
This integral converges for complex numbers with a positive real part. It has poles
for complex numbers with a negative real part (cf. Fig. F.2).
I
Figure F.1: The Gamma function.