示例：第一类贝塞耳函数

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示例：第一类贝塞耳函数

显示函数 J0、J1 和 Jn 之间的关系。也会显示这些函数和其缩放版本之间的关系。

1. 定义两个步长值域变量：

2. 绘制函数 J0 和 J1。在绘图中添加二阶函数 Jn：

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            <gridFrequency>7</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">J0</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">J1</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">Jn</id>
                  <sequence>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">m</id>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                  </sequence>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
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              <real xmlns="http://schemas.mathsoft.com/math50">-0.5</real>
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            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
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3. 创建绘图来显示 J0(y)=Jn(0,y)。重新设置刻度值来放大 x 轴以便显示更多详细信息：

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          <axisLine position="origin" positionticmark="2" legendWidth="60.74" />
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            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
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              <math>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">y</id>
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            <tickMarks display="true" />
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              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">J0</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">y</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
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            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">Jn</id>
                  <sequence>
                    <real>0</real>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">y</id>
                  </sequence>
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                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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              <real xmlns="http://schemas.mathsoft.com/math50">-0.25</real>
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              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
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4. 创建绘图来显示 J1(y)=Jn(1,y)。重新设置刻度值来放大 x 轴以便显示更多详细信息：

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            <gridLabels display="true" />
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              <math>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">y</id>
              </math>
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              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">J1</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">y</id>
                </apply>
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                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">Jn</id>
                  <sequence>
                    <real>1</real>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">y</id>
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5. 使用符号运算显示每个第一类贝塞尔函数和其缩放版本间的关系：

6. 创建绘图以显示：

J0.sc 包含复数元素，因此首先应用 Re 函数仅显示数的实数部分。

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            <gridFrequency>7</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">J0</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">y</id>
                </apply>
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              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
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            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">J0.sc</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">y</id>
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                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
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7. 计算出 J1 前两个峰值的坐标。使用函数 augment 和 localmax 来标识落在指定值域内的峰值：

函数 localmax 需要一个具有两列的输入矩阵。函数 augment 可用于创建这样的矩阵。

8. 使用函数 match 求出峰值的横坐标。减小 TOL 的值以获得最精确的结果：

9. 在图像上添加标记来标记前两个峰值：

步长值域变量的步长为 0.1。这意味着在 1/10 出现峰值，在此分别由函数 match 或 1.8 和 8.5 来标识元素索引。

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