Template:Infobox mathematics function/sandbox2
Jump to navigation
Jump to search
Gamma | |
---|---|
![]() The gamma function along part of the real axis | |
General Data | |
General definition | <math> \Gamma(z) = \int_0^\infty x^{z-1} e^{-x}\,dx \ </math>,<math>\qquad \Re(z) > 0\ </math> |
Deriver of General definition | Daniel Bernoulli |
Motivation of creation | Interpolation for factorial function |
Date of solution | 1720s |
Extends | Factorial function |
Fields of application | Probability, statistics, combinatorics |
Main applications | probability-distribution functions |
Domain and Range | |
Domain | <math>\mathbb{C}</math> - ℤ0- |
Codomain | <math>\mathbb{C}</math> - {0} |
Basic features | |
Parity | Not even and not odd |
Period | No |
analytic? | Yes |
meromorphic? | Yes |
holomorphic? | Yes except at ℤ0- |
Specific values | |
Maxima | No |
Minima | No |
Value at ℤ+ | <math>(n-1)!</math> |
Value at ℤ0- | Not defined |
Specific features | |
Root | No |
Critical point | <math>\supseteq</math> ℤ0- |
[[Inflection point|
| <math>\supseteq</math> ℤ0- |
[[Fixed point (mathematics)|
| <math>\supseteq</math> 1 |
Poles | <math>\supseteq</math> ℤ0- |
Transform | |
Corresponding transform | Mellin transform |
Corresponding transform formula | <math> \Gamma(z) = \{ \mathcal M e^{-x} \} (z).</math> |
The above documentation is transcluded from Template:Infobox mathematics function/sandbox2/doc. (edit | history) Editors can experiment in this template's sandbox (create | mirror) and testcases (create) pages. Please add categories to the /doc subpage. Subpages of this template. |