Gamma Function
Extend factorials between integers and discover recurrence, signs and poles.
Free theory articleExtend factorials between integers and discover recurrence, signs and poles.
Concept & interpretation
The Gamma function, denoted as Γ(z), is an extension of the factorial function to complex and real numbers. It shifts the argument by one such that Γ(n) = (n-1)! for positive integer n. The fundamental relation defining this extension is the recurrence relation Γ(z+1) = z Γ(z).
Interactive Experiment
Explore the properties of the Gamma function by using the interactive Gamma Function module. Adjust the controls to see how the recurrence relation connects points on the curve. Notice how the function grows for positive values and alternates signs with simple poles for negative integers.
- Set the "Argument x" to 0.5 to view the finite result 1.77245...
- Change the "Argument x" to 0 and observe the result transition to a pole.