関数
>
特殊関数
>
その他の特殊関数
> 例:ガンマ関数
例:ガンマ関数
1.
Γ
関数を使用して、
x
のさまざまな値に対してオイラーのガンマ関数をプロットします。
<region id="ID0EHNY6" top="96.000000000000014" left="38.400000000000006" height="27.791200000000003" width="139.42333333333335" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="218"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> <range> <sequence> <real>-5</real> <real>-4.9995</real> </sequence> <real>5</real> </range> </define> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EVNY6" top="115.20000000000002" left="38.400000000000006" height="288" width="576.59999999999991" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot background-type="white" origin-positioning="true"> <xyPlot> <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend /> <traces> <trace resultRef="220"> <traceStyle color="#FFED1D2F" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle> </trace> </traces> <graph-size width="457.4" height="230.4" /> <axes> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-5" end="5"> <axisLine position="origin" positionticmark="3" legendWidth="66.5166666666667" /> <axisGrid> <gridFrequency>11</gridFrequency> <gridLabels display="true" /> <gridLines /> <tickMarks display="true" /> </axisGrid> <axisLabel /> <markers> <marker resultRef="221" display="true" color="#FF000000" line-style="Dot" value="-1"> <real xmlns="http://schemas.mathsoft.com/math50">-1</real> </marker> <marker resultRef="223" display="true" color="#FF000000" line-style="Dot" value="-2"> <real xmlns="http://schemas.mathsoft.com/math50">-2</real> </marker> <marker resultRef="225" display="true" color="#FF000000" line-style="Dot" value="-3"> <real xmlns="http://schemas.mathsoft.com/math50">-3</real> </marker> <marker resultRef="227" display="true" color="#FF000000" line-style="Dot" value="0"> <real xmlns="http://schemas.mathsoft.com/math50">0</real> </marker> <marker resultRef="229" display="true" color="#FF000000" line-style="Dot" value="-4"> <real xmlns="http://schemas.mathsoft.com/math50">-4</real> </marker> <marker display="true" color="#FF000000" line-style="Dot" value="-5" /> </markers> <plotEquations> <plotEquation> <math resultRef="235"> <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </math> <math resultRef="236"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true"> <startValue> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </startValue> <secondTickValue resultRef="232"> <real xmlns="http://schemas.mathsoft.com/math50">-4</real> </secondTickValue> <endValue resultRef="234"> <real xmlns="http://schemas.mathsoft.com/math50">5</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-15" end="15"> <axisLine position="origin" positionticmark="5" legendWidth="90.34" /> <axisGrid> <gridFrequency>7</gridFrequency> <gridLabels display="true" /> <gridLines /> <tickMarks display="true" /> </axisGrid> <axisLabel /> <markers /> <plotEquations> <plotEquation> <math resultRef="243"> <apply xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve">Γ</id> <id xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </apply> </math> <math resultRef="244"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true"> <startValue resultRef="238"> <real xmlns="http://schemas.mathsoft.com/math50">-15</real> </startValue> <secondTickValue resultRef="240"> <real xmlns="http://schemas.mathsoft.com/math50">-10</real> </secondTickValue> <endValue resultRef="242"> <real xmlns="http://schemas.mathsoft.com/math50">15</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
関数は 0、-1、-2、...、などを除くすべての場所で解析的です。
2.
不完全
Γ
関数を使用して、
x
のさまざまな値に対して不完全ガンマ関数をプロットします。
<region id="ID0ERPY6" top="518.40000000000009" left="38.400000000000006" height="27.791200000000003" width="109.94333333333334" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="259"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> <range> <sequence> <real>0</real> <real>0.25</real> </sequence> <real>10</real> </range> </define> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0E6PY6" top="537.60000000000014" left="38.400000000000006" height="307.2" width="595.80000000000007" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot background-type="white" origin-positioning="true"> <xyPlot> <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend /> <traces> <trace resultRef="261"> <traceStyle color="#FFED1D2F" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle> </trace> <trace resultRef="262"> <traceStyle color="#FF068149" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle> </trace> <trace resultRef="263"> <traceStyle color="#FF2E3192" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle> </trace> </traces> <graph-size width="457.4" height="230.4" /> <axes> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-1" end="10"> <axisLine position="origin" positionticmark="0" legendWidth="66.5166666666667" /> <axisGrid> <gridFrequency>12</gridFrequency> <gridLabels display="true" /> <gridLines /> <tickMarks display="true" /> </axisGrid> <axisLabel /> <markers /> <plotEquations> <plotEquation> <math resultRef="270"> <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </math> <math resultRef="271"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true"> <startValue resultRef="265"> <real xmlns="http://schemas.mathsoft.com/math50">-1</real> </startValue> <secondTickValue resultRef="267"> <real xmlns="http://schemas.mathsoft.com/math50">0</real> </secondTickValue> <endValue resultRef="269"> <real xmlns="http://schemas.mathsoft.com/math50">10</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="2.5"> <axisLine position="origin" positionticmark="1" legendWidth="106.69" /> <axisGrid> <gridFrequency>6</gridFrequency> <gridLabels display="true" /> <gridLines /> <tickMarks display="true" /> </axisGrid> <axisLabel /> <markers /> <plotEquations> <plotEquation> <math resultRef="278"> <apply xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve">Γ</id> <sequence> <real>1</real> <id xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </sequence> </apply> </math> <math resultRef="279"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation> <math resultRef="280"> <apply xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve">Γ</id> <sequence> <real>2</real> <id xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </sequence> </apply> </math> <math resultRef="281"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation> <math resultRef="282"> <apply xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve">Γ</id> <sequence> <real>3</real> <id xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </sequence> </apply> </math> <math resultRef="283"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true"> <startValue resultRef="273"> <real xmlns="http://schemas.mathsoft.com/math50">0</real> </startValue> <secondTickValue resultRef="275"> <real xmlns="http://schemas.mathsoft.com/math50">0.5</real> </secondTickValue> <endValue resultRef="277"> <real xmlns="http://schemas.mathsoft.com/math50">2.5</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
3.
lnΓ
関数を使用して、
x
のさまざまな値に対してオイラーのガンマ関数の自然対数をプロットします。
<region id="ID0EWRY6" top="921.60000000000014" left="38.400000000000006" height="27.791200000000003" width="109.94333333333334" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="298"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span> </id> <range> <sequence> <real>0</real> <real>0.005</real> </sequence> <real>5</real> </range> </define> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EESY6" top="979.20000000000016" left="38.400000000000006" height="288" width="577" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot background-type="white" origin-positioning="true"> <xyPlot> <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend /> <traces> <trace resultRef="300"> <traceStyle color="#FFED1D2F" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle> </trace> </traces> <graph-size width="438.6" height="230.4" /> <axes> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-1" end="5"> <axisLine position="origin" positionticmark="1" legendWidth="66.5166666666667" /> <axisGrid> <gridFrequency>7</gridFrequency> <gridLabels display="true" /> <gridLines /> <tickMarks display="true" /> </axisGrid> <axisLabel /> <markers /> <plotEquations> <plotEquation> <math resultRef="307"> <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span> </id> </math> <math resultRef="308"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true"> <startValue resultRef="302"> <real xmlns="http://schemas.mathsoft.com/math50">-1</real> </startValue> <secondTickValue resultRef="304"> <real xmlns="http://schemas.mathsoft.com/math50">0</real> </secondTickValue> <endValue resultRef="306"> <real xmlns="http://schemas.mathsoft.com/math50">5</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-1" end="6"> <axisLine position="origin" positionticmark="1" legendWidth="103.32" /> <axisGrid> <gridFrequency>8</gridFrequency> <gridLabels display="true" /> <gridLines /> <tickMarks display="true" /> </axisGrid> <axisLabel /> <markers /> <plotEquations> <plotEquation> <math resultRef="315"> <apply xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve">lnΓ</id> <id xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span> </id> </apply> </math> <math resultRef="316"> <placeholder xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true"> <startValue resultRef="310"> <real xmlns="http://schemas.mathsoft.com/math50">-1</real> </startValue> <secondTickValue resultRef="312"> <real xmlns="http://schemas.mathsoft.com/math50">0</real> </secondTickValue> <endValue resultRef="314"> <real xmlns="http://schemas.mathsoft.com/math50">6</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
式をコピー
関連トピック
ガンマ関数
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