テンプレート:Infobox mathematical function/doc

数学的な関数の情報を集約するテンプレートです。

フォーマット

{{Infobox mathematical function
| name = 
| image= | imagesize= <!--(default 220px)--> | imagealt= | caption=
| generic_definition= | deriver= | motivation_of_creation= | date= | extends= | fields_of_application= | main_applications=
| domain= | codomain= | range=
| parity= | period= | analytic= | meromorphic= | holomorphic=
| zero= | plusinf= | minusinf= | max= | min= | vr1= | f1= | vr2= | f2= | vr3= | f3= | vr4= | f4= | vr5= | f5=
| asymptote= | root= | critical= | inflection= | fixed= | poles=
| reciprocal= | inverse= | derivative= | antiderivative= | other_related=
| taylor_series= | generalized_continued_fraction= | fourier_series=
| corresponding_transform= | corresponding_transform_formula=
| notes =
}}

使用例

{{Infobox mathematical function
| name = 正弦（Sine、サイン）関数
| image = Sine one period.svg

| general_definition = <math>\sin(\alpha) = \frac {\text{opposite}} {\text{hypotenuse}}</math>
| deriver=[[ヒッパルコス]]
| motivation_of_creation=[[測量]]、[[天文学]]
| date=[[古代ギリシア]]
| fields_of_application= [[三角法]]、[[積分変換]]、ほか多数
| domain=(−∞, +∞) {{smallsup|a}} |range=[−1, 1] {{smallsup|a}}
| parity=奇関数 | period=2{{pi}}
| zero=0 | max=2''k''{{pi}} + {{sfrac|{{pi}}|2}} において 1 {{smallsup|b}} |min=2''k''{{pi}} − {{sfrac|{{pi}}|2}} において −1 {{smallsup|b}}
| asymptote= |root=''k''{{pi}} |critical=''k''{{pi}} + {{sfrac|{{pi}}|2}} |inflection=''k''{{pi}} |fixed=0
| notes = {{ublist |{{sup|a}} [[実数]]について |{{sup|b}} ''k'' は [[整数]] }}

|reciprocal = [[Cosecant]]
|inverse = [[Arcsine]]
|derivative = <math>f'(x) = \cos(x) </math>
|antiderivative = <math>\int f(x)\,dx = -\cos(x) + C </math>
|generalized_continued_fraction = <math>
\cfrac{x}{1 + \cfrac{x^2}{2\cdot3-x^2 +
\cfrac{2\cdot3 x^2}{4\cdot5-x^2 +
\cfrac{4\cdot5 x^2}{6\cdot7-x^2 + \ddots}}}}.
</math>
|taylor_series= <math>
x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!}x^{2n+1}
</math>

|other_related= cos, tan, sec, cot
}}

{{Infobox mathematical function
| name = ガンマ（Gamma）関数
| image = Gamma plot.svg
| caption = 実軸の一部におけるガンマ関数

|general_definition = <math> \Gamma(z) = \int_0^\infty x^{z-1} e^{-x}\,dx \ </math>,<math>\qquad \Re(z) > 0\ </math>
| deriver = [[レオンハルト・オイラー]]
|motivation_of_creation = 階乗の [[補間]]
|extends = [[階乗]]
|date =[[1729年]]
|fields_of_application = [[確率]], [[統計]], [[組合せ数学]]
|main_applications = [[ガンマ分布]]

|domain={{math|'''C''' ∖ '''Z'''{{sub|≤ 0}}}} 
|range={{math|'''C''' ∖ {0}{{sup|}}}} 

|parity= なし
|period= なし
|analytic = Yes
|meromorphic = Yes
|holomorphic = Yes
|max= なし |min= なし |root= なし
|vr1={{math|''n'' ∈ '''Z'''{{sub|> 0}}}} |f1= {{math|(''n'' - 1) !}}
|vr2={{math|'''Z'''{{sub|≤ 0}}}} |f2= なし
|fixed={{math|⊇ 1}}
|poles = {{math|'''Z'''{{sub|≤ 0}}}} 

| corresponding_transform = [[メリン変換]]
| corresponding_transform_formula = <math>e^{-y}= \frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty} \Gamma(s) y^{-s}\;ds</math>
}}

追跡カテゴリ

• テンプレート:Clc

テンプレートデータ

テンプレート:Hidden begin テンプレート:TemplateData header <templatedata>{ "description": "数学的な関数の情報を集約するテンプレートです。", "params": { "name": { "description": "関数名", "type": "content", "required": true }, "image": { "description": "画像ファイル名", "type": "content", "required": false }, "imagesize": { "description": "画像サイズ", "type": "content", "required": false }, "imagealt": { "description": "画像代替テキスト", "type": "content", "required": false }, "caption": { "description": "画像のキャプション", "type": "content", "required": false }, "generic_definition": { "description": "関数の一般的な定義", "type": "content", "required": false }, "deriver": { "description": "考案・導入した人物", "type": "content", "required": false }, "motivation_of_creation": { "description": "背景・動機", "type": "content", "required": false }, "date": { "description": "導入された時期", "type": "content", "required": false }, "extends": { "description": "拡張元の関数", "type": "content", "required": false }, "fields_of_application": { "description": "応用されている分野・領域", "type": "content", "required": false }, "main_applications": { "description": "主な応用例", "type": "content", "required": false }, "domain": { "description": "定義域", "type": "content", "required": false }, "codomain": { "description": "終域", "type": "content", "required": false }, "range": { "description": "値域", "type": "content", "required": false }, "parity": { "description": "関数の偶奇性", "type": "content", "required": false }, "period": { "description": "関数の周期性", "type": "content", "required": false }, "analytic": { "description": "解析関数か否か", "type": "content", "required": false }, "meromorphic": { "description": "有理型関数か否か", "type": "content", "required": false }, "holomorphic": { "description": "正則関数か否か", "type": "content", "required": false }, "zero": { "description": "原点での値", "type": "content", "required": false }, "plusinf": { "description": "正の無限大における極限値", "type": "content", "required": false }, "minusinf": { "description": "負の無限大における極限値", "type": "content", "required": false }, "max": { "description": "極大値", "type": "content", "required": false }, "min": { "description": "極小値", "type": "content", "required": false }, "vr1": { "description": "特筆すべき値をとる点1", "type": "content", "required": false }, "f1": { "description": "vr1での値", "type": "content", "required": false }, "vr2": { "description": "特筆すべき値をとる点2", "type": "content", "required": false }, "f2": { "description": "vr2での値", "type": "content", "required": false }, "vr3": { "description": "特筆すべき値をとる点3", "type": "content", "required": false }, "f3": { "description": "vr3での値", "type": "content", "required": false }, "vr4": { "description": "特筆すべき値をとる点4", "type": "content", "required": false }, "f4": { "description": "vr4での値", "type": "content", "required": false }, "vr5": { "description": "特筆すべき値をとる点5", "type": "content", "required": false }, "f5": { "description": "vr5での値", "type": "content", "required": false }, "asymptote": { "description": "漸近線", "type": "content", "required": false }, "root": { "description": "関数の零点", "type": "content", "required": false }, "critical": { "description": "関数の臨界点", "type": "content", "required": false }, "inflection": { "description": "関数の変曲点", "type": "content", "required": false }, "fixed": { "description": "関数の不動点", "type": "content", "required": false }, "poles": { "description": "関数の極", "type": "content", "required": false }, "reciprocal": { "description": "逆数", "type": "content", "required": false }, "inverse": { "description": "逆関数", "type": "content", "required": false }, "derivative": { "description": "導関数", "type": "content", "required": false }, "antiderivative": { "description": "原始関数", "type": "content", "required": false }, "other_related": { "description": "その他の関連のある関数", "type": "content", "required": false }, "taylor_series": { "description": "テイラー級数", "type": "content", "required": false }, "generalized_continued_fraction": { "description": "一般化連分数", "type": "content", "required": false }, "fourier_series": { "description": "フーリエ級数", "type": "content", "required": false }, "corresponding_transform": { "description": "対応する変換操作", "type": "content", "required": false }, "corresponding_transform_formula": { "description": "対応する変換操作の変換公式", "type": "content", "required": false }, "notes": { "description": "注", "type": "content", "required": false } } }</templatedata> テンプレート:Hidden end