範例：第一類與第二類漢克函數

函數 > 特殊函數 > Bessel 函數 > 範例：第一類與第二類漢克函數

範例：第一類與第二類漢克函數

顯示漢克函數 H1 和 H2 與貝賽耳函數 Jn 和 Yn 之間的關係。另顯示這些函數與其成比例版本之間的關係。

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1. 使用符號計算顯示 H1、Jn 及 Yn 之間的關係。

2. 使用符號計算顯示 H2、Jn 及 Yn 之間的關係。

◦ H1 與 H2 的實數元件具有相同的值與正負號。

◦ H1 與 H2 的虛數元件具有相同的值，但正負號相反。

3. 請注意 H1 與 H2 之間，下列的其他兩項重要關係。

4. 建立繪圖以視覺方式顯示 |H1|=|H2|。

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        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="2">
          <axisLine position="origin" positionticmark="0" legendWidth="125.873333333333" />
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            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <absval />
                  <apply>
                    <id labels="FUNCTION" xml:space="preserve">H1</id>
                    <sequence>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</id>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
                    </sequence>
                  </apply>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <absval />
                  <apply>
                    <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">H2</id>
                    <sequence>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</id>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
                    </sequence>
                  </apply>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
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5. 建立繪圖以顯示 H1、Jn 及 Yn 之間的關係。

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            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <absval />
                  <apply>
                    <id labels="FUNCTION" xml:space="preserve">H1</id>
                    <sequence>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</id>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
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                </apply>
              </math>
              <math>
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            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">Jn</id>
                  <sequence>
                    <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</id>
                    <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
                  </sequence>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">Yn</id>
                  <sequence>
                    <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</id>
                    <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
                  </sequence>
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              <math>
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6. 使用符號計算顯示漢克函數與其成比例版本之間的關係。

7. 建立繪圖以顯示：

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              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <absval />
                  <apply>
                    <mult />
                    <apply>
                      <id labels="FUNCTION" xml:space="preserve">H1</id>
                      <sequence>
                        <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</id>
                        <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
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                        <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
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                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
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            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <absval />
                  <apply>
                    <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">H1.sc</id>
                    <sequence>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</id>
                      <id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</id>
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8. 建立繪圖以顯示：

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漢克函數

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