Difference between revisions of "Template:Infobox mathematics function/sandbox2"

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imported>Hooman Mallahzadeh
imported>Hooman Mallahzadeh
 
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Latest revision as of 09:39, 9 October 2020

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Gamma
Gamma plot.svg
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 definitionDaniel Bernoulli
Motivation of creationInterpolation for factorial function
Date of solution1720s
ExtendsFactorial function
Fields of applicationProbability, statistics, combinatorics
Main applicationsprobability-distribution functions
Domain and Range
Domain<math>\mathbb{C}</math> - ℤ0-
Codomain<math>\mathbb{C}</math> - {0}
Basic features
ParityNot even and not odd
PeriodNo
analytic?Yes
meromorphic?Yes
holomorphic?Yes except at ℤ0-
Specific values
MaximaNo
MinimaNo
Value at +<math>(n-1)!</math>
Value at 0-Not defined
Specific features
RootNo
Critical point<math>\supseteq</math> ℤ0-
[[Inflection point|
  1. REDIRECT Template:Wrap]]
<math>\supseteq</math> ℤ0-
[[Fixed point (mathematics)|
  • REDIRECT Template:Wrap]]
  • <math>\supseteq</math> 1
    Poles<math>\supseteq</math> ℤ0-
    Transform
    Corresponding transformMellin transform
    Corresponding transform formula<math> \Gamma(z) = \{ \mathcal M e^{-x} \} (z).</math>