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 = | + | | label7 = Date of solution |
| − | | data7 = {{{ | + | | data7 = {{{date|}}} |
| + | | label8 = Extends | ||
| + | | data8 = {{{extends|}}} | ||
| − | |||
| − | |||
| − | | label9 = | + | | label9 = Fields of application |
| − | | data9 = {{{ | + | | data9 = {{{fields_of_application|}}} |
| − | | | + | | label10 = Main applications |
| + | | data10 = {{{main_applications|}}} | ||
| + | |||
| + | | header11 = {{#if:{{{domain|}}}{{{codomain|}}}{{{range|}}} | ||
| Domain and Range }} | | Domain and Range }} | ||
| − | | | + | | label12 = [[Domain of a function|Domain]] |
| − | | | + | | data12 = {{{domain|}}} |
| − | | | + | | label13 = [[Codomain]] |
| − | | | + | | data13 = {{{codomain|}}} |
| − | | | + | | label14 = [[Range of a function|Range]] |
| − | | | + | | data14 = {{{range|}}} |
| − | | | + | | header15 = {{#if:{{{parity|}}}{{{period|}}}{{{analytic|}}}{{{meromorphic|}}}{{{holomorphic|}}} |
| Basic features }} | | Basic features }} | ||
| − | | | + | | label16 = [[Even and odd functions|Parity]] |
| − | | | + | | data16 = {{{parity|}}} |
| − | | | + | | label17 = [[Period (mathematics)|Period]] |
| − | | | + | | data17 = {{{period|}}} |
| − | | | + | | label18 = analytic? |
| − | | | + | | data18 = {{{analytic|}}} |
| − | | | + | | label19 = meromorphic? |
| − | | | + | | data19 = {{{meromorphic|}}} |
| − | | | + | | label20 = holomorphic? |
| − | | | + | | data20 = {{{holomorphic|}}} |
| − | | | + | | header21 = {{#if:{{{zero|}}}{{{plusinf|}}}{{{minusinf|}}}{{{max|}}}{{{min|}}}{{{vr1|}}} |
| Specific values }} | | Specific values }} | ||
| − | | | + | | label22 = [[y-intercept|At zero]] |
| − | | | + | | data22 = {{{zero|}}} |
| − | | | + | | label23 = Value at +{{lower|0.25em|{{resize|130%|∞}}}} |
| − | | | + | | data23 = {{{plusinf|}}} |
| − | | | + | | label24 = Value at -{{lower|0.25em|{{resize|130%|∞}}}} |
| − | | | + | | data24 = {{{minusinf|}}} |
| − | | | + | | label25 = Maxima |
| − | | | + | | data25 = {{{max|}}} |
| − | | | + | | label26 = Minima |
| − | | | + | | data26 = {{{min|}}} |
| − | | | + | | label27 = Value at {{{vr1|}}} |
| − | | | + | | data27 = {{{f1|}}} |
| − | | | + | | label28 = Value at {{{vr2|}}} |
| − | | | + | | data28 = {{{f2|}}} |
| − | | | + | | label29 = Value at {{{vr3|}}} |
| − | | | + | | data29 = {{{f3|}}} |
| − | | | + | | label30 = Value at {{{vr4|}}} |
| − | | | + | | data30 = {{{f4|}}} |
| − | | | + | | label31 = Value at {{{vr5|}}} |
| − | | | + | | data31 = {{{f5|}}} |
| − | | | + | | header32 = {{#if:{{{asymptote|}}}{{{root|}}}{{{critical|}}}{{{inflection|}}}{{{fixed|}}}{{{poles|}}} |
| Specific features }} | | Specific features }} | ||
| − | | | + | | label33 = [[Asymptote]] |
| − | | | + | | data33 = {{{asymptote|}}} |
| − | | | + | | label34 = [[Root of a function|Root]] |
| − | | | + | | data34 = {{{root|}}} |
| − | | | + | | label35 = [[Critical point (mathematics)|Critical point]] |
| − | | | + | | data35 = {{{critical|}}} |
| − | | | + | | label36 = [[Inflection point|{{allow wrap|Inflection point}}]] |
| − | | | + | | data36 = {{{inflection|}}} |
| − | | | + | | label37 = [[Fixed point (mathematics)|{{allow wrap|Fixed point}}]] |
| − | | | + | | data37 = {{{fixed|}}} |
| − | | | + | | label38 = [[Zeros and poles|Poles]] |
| − | | | + | | data38 = {{{poles|}}} |
| − | | | + | | header39 = {{#if:{{{corresponding_transform|}}}{{{corresponding_transform_formula|}}} |
| Transform }} | | Transform }} | ||
| − | + | | label40 = Corresponding transform | |
| − | + | | data40 = {{{corresponding_transform|}}} | |
| − | |||
| − | | label40 = Corresponding transform | ||
| − | | data40 = {{{ | ||
| − | |||
| − | |||
| + | | label41 = Corresponding transform formula | ||
| + | | data41 = {{{corresponding_transform_formula|}}} | ||
| − | | | + | | data42 = {{#if:{{{notes|}}} |<hr/>{{smaller|{{{notes}}}}} }} |
}}</includeonly><noinclude>{{Documentation}}</noinclude> | }}</includeonly><noinclude>{{Documentation}}</noinclude> | ||
Latest revision as of 09:39, 9 October 2020
| 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 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. |