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

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imported>Hooman Mallahzadeh
imported>Hooman Mallahzadeh
 
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|  data6  = {{{motivation_of_creation|}}}
 
|  data6  = {{{motivation_of_creation|}}}
  
| label7  = Extends
+
| label7  = Date of solution
|  data7  = {{{extends|}}}
+
|  data7  = {{{date|}}}
  
 +
| label8  =  Extends
 +
|  data8  = {{{extends|}}}
  
| label8  =  Fields_of_application
 
|  data8  = {{{fields_of_application|}}}
 
  
| label9  =  Main applications
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| label9  =  Fields of application
|  data9  = {{{mian_applications|}}}
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|  data9  = {{{fields_of_application|}}}
  
| header10 = {{#if:{{{domain|}}}{{{codomain|}}}{{{range|}}}
+
| label10  =  Main applications
 +
|  data10  = {{{main_applications|}}}
 +
 
 +
| header11 = {{#if:{{{domain|}}}{{{codomain|}}}{{{range|}}}
 
| Domain and Range }}
 
| Domain and Range }}
  
  
| label11   = [[Domain of a function|Domain]]
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| label12   = [[Domain of a function|Domain]]
data11   = {{{domain|}}}
+
data12   = {{{domain|}}}
  
| label12   = [[Codomain]]
+
| label13   = [[Codomain]]
data12   = {{{codomain|}}}
+
data13   = {{{codomain|}}}
  
| label13   = [[Range of a function|Range]]
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| label14   = [[Range of a function|Range]]
data13   = {{{range|}}}
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data14   = {{{range|}}}
  
  
  
  
| header14 = {{#if:{{{parity|}}}{{{period|}}}{{{analytic|}}}{{{meromorphic|}}}{{{holomorphic|}}}
+
| header15 = {{#if:{{{parity|}}}{{{period|}}}{{{analytic|}}}{{{meromorphic|}}}{{{holomorphic|}}}
 
             | Basic features }}
 
             | Basic features }}
  
| label15   = [[Even and odd functions|Parity]]
+
| label16   = [[Even and odd functions|Parity]]
data15   = {{{parity|}}}
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data16   = {{{parity|}}}
  
| label16   = [[Period (mathematics)|Period]]
+
| label17   = [[Period (mathematics)|Period]]
data16   = {{{period|}}}
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data17   = {{{period|}}}
  
| label17   = analytic?
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| label18   = analytic?
data17   = {{{analytic|}}}
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data18   = {{{analytic|}}}
  
| label18   =  meromorphic?
+
| label19   =  meromorphic?
data18   = {{{meromorphic|}}}
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data19   = {{{meromorphic|}}}
  
| label19   =  holomorphic?
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| label20   =  holomorphic?
data19   = {{{holomorphic|}}}
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data20   = {{{holomorphic|}}}
  
| header20 = {{#if:{{{zero|}}}{{{plusinf|}}}{{{minusinf|}}}{{{max|}}}{{{min|}}}{{{vr1|}}}
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| header21 = {{#if:{{{zero|}}}{{{plusinf|}}}{{{minusinf|}}}{{{max|}}}{{{min|}}}{{{vr1|}}}
 
               | Specific values }}
 
               | Specific values }}
  
| label21 = [[y-intercept|At zero]]
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| label22 = [[y-intercept|At zero]]
data21 = {{{zero|}}}
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data22 = {{{zero|}}}
  
| label22 = Value at +{{lower|0.25em|{{resize|130%|∞}}}}
+
| label23 = Value at +{{lower|0.25em|{{resize|130%|∞}}}}
data22 = {{{plusinf|}}}
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data23 = {{{plusinf|}}}
  
| label23 = Value at -{{lower|0.25em|{{resize|130%|∞}}}}
+
| label24 = Value at -{{lower|0.25em|{{resize|130%|∞}}}}
data23 = {{{minusinf|}}}
+
data24 = {{{minusinf|}}}
  
| label24 = Maxima
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| label25 = Maxima
data24 = {{{max|}}}
+
data25 = {{{max|}}}
  
| label25 = Minima
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| label26 = Minima
data25 = {{{min|}}}
+
data26 = {{{min|}}}
  
| label26 = Value at {{{vr1|}}}
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| label27 = Value at {{{vr1|}}}
data26 = {{{f1|}}}
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data27 = {{{f1|}}}
  
| label27 = Value at {{{vr2|}}}
+
| label28 = Value at {{{vr2|}}}
data27 = {{{f2|}}}
+
data28 = {{{f2|}}}
  
| label28 = Value at {{{vr3|}}}
+
| label29 = Value at {{{vr3|}}}
data28 = {{{f3|}}}
+
data29 = {{{f3|}}}
  
| label29 = Value at {{{vr4|}}}
+
| label30 = Value at {{{vr4|}}}
data29 = {{{f4|}}}
+
data30 = {{{f4|}}}
  
| label30 = Value at {{{vr5|}}}
+
| label31 = Value at {{{vr5|}}}
data30 = {{{f5|}}}
+
data31 = {{{f5|}}}
  
| header31 = {{#if:{{{asymptote|}}}{{{root|}}}{{{critical|}}}{{{inflection|}}}{{{fixed|}}}{{{poles|}}}
+
| header32 = {{#if:{{{asymptote|}}}{{{root|}}}{{{critical|}}}{{{inflection|}}}{{{fixed|}}}{{{poles|}}}
 
               | Specific features }}
 
               | Specific features }}
  
| label32 = [[Asymptote]]
+
| label33 = [[Asymptote]]
data32 = {{{asymptote|}}}
+
data33 = {{{asymptote|}}}
  
| label33 = [[Root of a function|Root]]
+
| label34 = [[Root of a function|Root]]
data33 = {{{root|}}}
+
data34 = {{{root|}}}
  
| label34 = [[Critical point (mathematics)|Critical point]]
+
| label35 = [[Critical point (mathematics)|Critical point]]
data34 = {{{critical|}}}
+
data35 = {{{critical|}}}
  
| label35 = [[Inflection point|{{allow wrap|Inflection point}}]]
+
| label36 = [[Inflection point|{{allow wrap|Inflection point}}]]
data35 = {{{inflection|}}}
+
data36 = {{{inflection|}}}
  
| label36 = [[Fixed point (mathematics)|{{allow wrap|Fixed point}}]]
+
| label37 = [[Fixed point (mathematics)|{{allow wrap|Fixed point}}]]
data36 = {{{fixed|}}}
+
data37 = {{{fixed|}}}
  
| label37   =  [[Zeros and poles|Poles]]
+
| label38   =  [[Zeros and poles|Poles]]
data37   = {{{poles|}}}
+
data38   = {{{poles|}}}
  
| header38 = {{#if:{{{corresponding_transform|}}}{{{corresponding_transform_formula|}}}
+
| header39 = {{#if:{{{corresponding_transform|}}}{{{corresponding_transform_formula|}}}
 
               | Transform }}
 
               | Transform }}
  
| label39  =  Corresponding transform
+
| label40  =  Corresponding transform
|  data39  = {{{corresponding_transform|}}}
+
|  data40  = {{{corresponding_transform|}}}
 
 
| label40  =  Corresponding transform formula
 
|  data40  = {{{corresponding_transform_formula|}}}
 
 
 
 
 
  
 +
| label41  =  Corresponding transform formula
 +
|  data41  = {{{corresponding_transform_formula|}}}
  
data50 = {{#if:{{{notes|}}} |<hr/>{{smaller|{{{notes}}}}} }}
+
data42 = {{#if:{{{notes|}}} |<hr/>{{smaller|{{{notes}}}}} }}
  
 
}}</includeonly><noinclude>{{Documentation}}</noinclude>
 
}}</includeonly><noinclude>{{Documentation}}</noinclude>

Latest revision as of 09:39, 9 October 2020

50px Template documentation[view] [edit] [history] [purge]
Gamma
File: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>