Definition
The gamma function is a special function defined for all complex numbers except non-positive numbers. It is also known as the The Euler integral of the second kind. It is denoted by the uppercase Greek letter “Gamma”
The gamma function is defined by Analytic Continuation. It is a Meromorphic function with no zeros and with simple poles of residue
For every positive integers
Functional Relations
- Recurrence:
- Euler’s reflection formula:
- Legendre duplication formula:
- Gauss’s multiplication formula:
Other Properties
- Complex conjugate:
- Absolute value:
- Derivative: