範例：第一類修正過的 Bessel 函數

函數 > 特殊函數 > Bessel 函數 > 範例：第一類修正過的 Bessel 函數

顯示函數 I0、I1 及 In 之間的關係。另顯示這些函數與其成比例版本之間的關係。

1. 定義兩個步距範圍變數：

2. 繪製函數 I0 與 I1。將第 2 階函數 In 新增至繪圖：

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                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
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              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">In</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>
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3. 繪製第 5 階與第 8 階函數 In：

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                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
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                      <plus />
                      <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">m</id>
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                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
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• In 函數的階數愈高，從零到無限大的轉移會變得愈急劇。

• 只有函數 I0 的原點位於 (x=0,y=1)。其他所有階數的原點位於 (x=0,y=0).

4. 建立繪圖以顯示 I0(y)=In(0,y)。重設刻度線值放大 x 軸，以顯示更多細節：

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5. 建立繪圖以顯示 I1(y)=In(1,y)。重設刻度線值放大 x 軸，以顯示更多細節：

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6. 使用符號計算，以顯示每個函數與其成比例版本之間的關係：

7. 使用繪圖以顯示：

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第一類修正過的 Bessel 函數沒有尖峰。

相關主題

修正過 (雙曲線的) 的 Bessel 函數

這是否有幫助?