MathLiveGamma function (Euler integral of the second kind)
Defines the gamma function as an integral that extends the factorial to real and complex numbers, with the argument shifted down by one so that Gamma(n) equals (n-1)! for positive integers. It is used wherever factorials of non-integer values appear, such as in probability, statistics and complex analysis.
\Gamma\left(z\right) = \int_{0}^{\infty} t^{z-1} e^{-t} \, \mathrm{d}tWhat the symbols mean
| the gamma function evaluated at z | |
| complex number with positive real part (argument of the function) | |
| integration variable | |
| Euler's number, the base of the natural logarithm |
About this formula
- FieldMathematics
- TopicSpecial functions
- LevelUniversity
- Also calledgamma function integral, complete gamma function, Euler integral of the second kind, gamma function definition, factorial extension integral, Gamma(z) integral definition
- SourceWikidata Q190573
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