Пример. Полиномиальные функции

Функции > Специальные функции > Другие специальные функции > Пример. Полиномиальные функции

Полином Эрмита

1. Используйте функцию Her, чтобы построить график значений полинома Эрмита при различных значениях x.

Щелкните для копирования этого выражения

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 <math resultRef="260">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Her</id>
 <sequence>
 <real>1</real>
 <id xml:space="preserve">
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 <math resultRef="262">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Her</id>
 <sequence>
 <real>2</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="263">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="264">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Her</id>
 <sequence>
 <real>3</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="265">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 </plotEquation>
 <plotEquation>
 <math resultRef="266">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Her</id>
 <sequence>
 <real>4</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript>
 </id>
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 </math>
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 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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Полином Лагерра

1. Используйте функцию Lag, чтобы построить график значений полинома Лагерра при различных значениях x.

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 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript>
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 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
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 <axisLabel />
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 <plotEquation>
 <math resultRef="303">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Lag</id>
 <sequence>
 <real>1</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript>
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 </math>
 <math resultRef="304">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 <plotEquation>
 <math resultRef="305">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Lag</id>
 <sequence>
 <real>2</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript>
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 </sequence>
 </apply>
 </math>
 <math resultRef="306">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="307">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Lag</id>
 <sequence>
 <real>3</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="308">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="309">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Lag</id>
 <sequence>
 <real>4</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript>
 </id>
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 <math resultRef="310">
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 </math>
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 <real xmlns="http://schemas.mathsoft.com/math50">-2</real>
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 <real xmlns="http://schemas.mathsoft.com/math50">4</real>
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Полином Лежандра

1. Используйте функцию Leg, чтобы построить график значений полинома Лежандра при различных значениях x.

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 <math resultRef="339">
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">
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 <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-1" end="1">
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 <gridFrequency>3</gridFrequency>
 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
 </axisGrid>
 <axisLabel />
 <markers />
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 <math resultRef="347">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Leg</id>
 <sequence>
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 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
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 <math resultRef="349">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Leg</id>
 <sequence>
 <real>2</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="350">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 </plotEquation>
 <plotEquation>
 <math resultRef="351">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Leg</id>
 <sequence>
 <real>3</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="352">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 </plotEquation>
 <plotEquation>
 <math resultRef="353">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Leg</id>
 <sequence>
 <real>4</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
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 <real xmlns="http://schemas.mathsoft.com/math50">1</real>
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Полином Чебышева первого и второго рода

1. Используйте функцию Tcheb, чтобы построить график значений полинома Чебышева первого рода при различных значениях x.

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 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Tcheb</id>
 <sequence>
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 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="382">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
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 <plotEquation>
 <math resultRef="383">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Tcheb</id>
 <sequence>
 <real>3</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="384">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 <plotEquation>
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 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Tcheb</id>
 <sequence>
 <real>4</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
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 <math resultRef="386">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
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 </endValue>
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 </yAxis>
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 </xyPlot>
 </plot>
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2. Используйте функцию Ucheb, чтобы построить график значений полинома Чебышева второго рода при различных значениях x.

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 <math resultRef="414">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 <plotEquation>
 <math resultRef="415">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Ucheb</id>
 <sequence>
 <real>2</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="416">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="417">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Ucheb</id>
 <sequence>
 <real>3</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="418">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="419">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Ucheb</id>
 <sequence>
 <real>4</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="420">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="421">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Ucheb</id>
 <sequence>
 <real>5</real>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">3</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="422">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
 <startValue resultRef="408">
 <real xmlns="http://schemas.mathsoft.com/math50">-6</real>
 </startValue>
 <secondTickValue resultRef="410">
 <real xmlns="http://schemas.mathsoft.com/math50">-4</real>
 </secondTickValue>
 <endValue resultRef="412">
 <real xmlns="http://schemas.mathsoft.com/math50">6</real>
 </endValue>
 </xyDomain>
 </yAxis>
 </axes>
 </xyPlot>
 </plot>
</region>

Полином Якоби

1. Используйте функцию Jac, чтобы построить график значений полинома Якоби с параметрами a и b при различных значениях x.

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 <axes>
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 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
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 <axisLabel />
 <markers />
 <plotEquations>
 <plotEquation>
 <math resultRef="453">
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">
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 <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-10" end="10">
 <axisLine position="origin" positionticmark="2" legendWidth="152.25" />
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 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
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 <markers />
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 <plotEquation>
 <math resultRef="461">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Jac</id>
 <sequence>
 <real>1</real>
 <id xml:space="preserve">a</id>
 <id xml:space="preserve">b</id>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">4</Subscript>
 </id>
 </sequence>
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 </math>
 <math resultRef="462">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="463">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Jac</id>
 <sequence>
 <real>2</real>
 <id xml:space="preserve">a</id>
 <id xml:space="preserve">b</id>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">4</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="464">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 </plotEquation>
 <plotEquation>
 <math resultRef="465">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Jac</id>
 <sequence>
 <real>3</real>
 <id xml:space="preserve">a</id>
 <id xml:space="preserve">b</id>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">4</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="466">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="467">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">Jac</id>
 <sequence>
 <real>4</real>
 <id xml:space="preserve">a</id>
 <id xml:space="preserve">b</id>
 <id xml:space="preserve">
 x<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">4</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="468">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
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 <real xmlns="http://schemas.mathsoft.com/math50">-10</real>
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 <real xmlns="http://schemas.mathsoft.com/math50">-5</real>
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 </yAxis>
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 </xyPlot>
 </plot>
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