函數
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特殊函數
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範例：伽瑪函數
範例：伽瑪函數
1.
使用
Γ
函數在不同的
x
值上繪製尤拉伽瑪函數。
<region id="ID0E61ZDB" top="96.000000000000014" left="38.400000000000006" height="27.791200000000003" width="139.42333333333335" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="218" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> <range xml:lang="zh_TW"> <sequence xml:lang="zh_TW"> <real xml:lang="zh_TW">-5</real> <real xml:lang="zh_TW">-4.9995</real> </sequence> <real xml:lang="zh_TW">5</real> </range> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0ER2ZDB" top="115.20000000000002" left="38.400000000000006" height="288" width="576.59999999999991" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot background-type="white" origin-positioning="true" xml:lang="zh_TW"> <xyPlot xml:lang="zh_TW"> <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend xml:lang="zh_TW" /> <traces xml:lang="zh_TW"> <trace resultRef="220" xml:lang="zh_TW"> <traceStyle color="#FFED1D2F" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> </traces> <graph-size width="457.4" height="230.4" xml:lang="zh_TW" /> <axes xml:lang="zh_TW"> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-5" end="5" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="3" legendWidth="66.5166666666667" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">11</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW"> <marker resultRef="221" display="true" color="#FF000000" line-style="Dot" value="-1" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-1</real> </marker> <marker resultRef="223" display="true" color="#FF000000" line-style="Dot" value="-2" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-2</real> </marker> <marker resultRef="225" display="true" color="#FF000000" line-style="Dot" value="-3" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-3</real> </marker> <marker resultRef="227" display="true" color="#FF000000" line-style="Dot" value="0" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0</real> </marker> <marker resultRef="229" display="true" color="#FF000000" line-style="Dot" value="-4" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-4</real> </marker> <marker display="true" color="#FF000000" line-style="Dot" value="-5" xml:lang="zh_TW" /> </markers> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="235" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </math> <math resultRef="236" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </startValue> <secondTickValue resultRef="232" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-4</real> </secondTickValue> <endValue xml:lang="zh_TW" resultRef="234"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">5</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-15" end="15" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="5" legendWidth="90.34" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">7</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="243" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW">Γ</id> <id xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </apply> </math> <math resultRef="244" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue resultRef="238" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-15</real> </startValue> <secondTickValue resultRef="240" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-10</real> </secondTickValue> <endValue xml:lang="zh_TW" resultRef="242"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">15</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
此函數會在所有的位置上進行分析，但在 0、-1、-2 等位置上則除外。
2.
使用不完整的
Γ
函數在不同的
x
值上繪製不完整伽瑪函數。
<region id="ID0EV4ZDB" top="518.40000000000009" left="38.400000000000006" height="27.791200000000003" width="109.94333333333334" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="259" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> <range xml:lang="zh_TW"> <sequence xml:lang="zh_TW"> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0.25</real> </sequence> <real xml:lang="zh_TW">10</real> </range> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EH5ZDB" top="537.60000000000014" left="38.400000000000006" height="307.2" width="595.80000000000007" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot background-type="white" origin-positioning="true" xml:lang="zh_TW"> <xyPlot xml:lang="zh_TW"> <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend xml:lang="zh_TW" /> <traces xml:lang="zh_TW"> <trace resultRef="261" xml:lang="zh_TW"> <traceStyle color="#FFED1D2F" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> <trace resultRef="262" xml:lang="zh_TW"> <traceStyle color="#FF068149" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">lines</traceStyle> </trace> <trace resultRef="263" xml:lang="zh_TW"> <traceStyle color="#FF2E3192" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> </traces> <graph-size width="457.4" height="230.4" xml:lang="zh_TW" /> <axes xml:lang="zh_TW"> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-1" end="10" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="0" legendWidth="66.5166666666667" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">12</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="270" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </math> <math resultRef="271" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue resultRef="265" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-1</real> </startValue> <secondTickValue resultRef="267" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0</real> </secondTickValue> <endValue xml:lang="zh_TW" resultRef="269"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">10</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="2.5" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="1" legendWidth="106.69" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">6</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="278" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW">Γ</id> <sequence xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <id xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </sequence> </apply> </math> <math resultRef="279" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math resultRef="280" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW">Γ</id> <sequence xml:lang="zh_TW"> <real xml:lang="zh_TW">2</real> <id xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </sequence> </apply> </math> <math resultRef="281" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math resultRef="282" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW">Γ</id> <sequence xml:lang="zh_TW"> <real xml:lang="zh_TW">3</real> <id xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </sequence> </apply> </math> <math resultRef="283" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue resultRef="273" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0</real> </startValue> <secondTickValue resultRef="275" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0.5</real> </secondTickValue> <endValue xml:lang="zh_TW" resultRef="277"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">2.5</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
3.
使用
lnΓ
函數在不同的
x
值上繪製尤拉伽瑪函數的自然對數。
<region id="ID0EGA1DB" top="921.60000000000014" left="38.400000000000006" height="27.791200000000003" width="109.94333333333334" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="298" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span> </id> <range xml:lang="zh_TW"> <sequence xml:lang="zh_TW"> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0.005</real> </sequence> <real xml:lang="zh_TW">5</real> </range> </define> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EYA1DB" top="979.20000000000016" left="38.400000000000006" height="288" width="577" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot background-type="white" origin-positioning="true" xml:lang="zh_TW"> <xyPlot xml:lang="zh_TW"> <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend xml:lang="zh_TW" /> <traces xml:lang="zh_TW"> <trace resultRef="300" xml:lang="zh_TW"> <traceStyle color="#FFED1D2F" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> </traces> <graph-size width="438.6" height="230.4" xml:lang="zh_TW" /> <axes xml:lang="zh_TW"> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-1" end="5" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="1" legendWidth="66.5166666666667" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">7</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="307" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span> </id> </math> <math resultRef="308" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue resultRef="302" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-1</real> </startValue> <secondTickValue resultRef="304" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0</real> </secondTickValue> <endValue xml:lang="zh_TW" resultRef="306"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">5</real> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-1" end="6" xml:lang="zh_TW"> <axisLine position="origin" positionticmark="1" legendWidth="103.32" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">8</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="315" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW">lnΓ</id> <id xml:space="preserve" xml:lang="zh_TW"> <Span xml:lang="zh_TW" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">x<Subscript xml:lang="zh_TW" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span> </id> </apply> </math> <math resultRef="316" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue resultRef="310" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">-1</real> </startValue> <secondTickValue resultRef="312" xml:lang="zh_TW"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0</real> </secondTickValue> <endValue xml:lang="zh_TW" resultRef="314"> <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">6</real> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
複製運算式
