狄喇克函數

函數 > 符號函數 > 狄喇克函數

狄喇克函數

• Δ(x) - 傳回狄喇克 (單位脈衝) 函數，定義如下︰

<region id="ID0EIU4BB" actualWidth="66.353333333333339" actualHeight="25.6" top="19.200000000000003" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="5"> <apply xmlns="http://schemas.mathsoft.com/math50"> <equal /> <apply> <id xml:space="preserve">Δ</id> <id xml:space="preserve">x</id> </apply> <real>0</real> </apply> </math> </region>	if	<region id="ID0EKV4BB" actualWidth="37.176666666666662" actualHeight="25.6" top="19.200000000000003" left="230.40000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="6"> <apply xmlns="http://schemas.mathsoft.com/math50"> <notEqual /> <id xml:space="preserve">x</id> <real>0</real> </apply> </math> </region>
以及
<region id="ID0EHX4BB" actualWidth="104.39833333333335" actualHeight="56.800000000000004" top="76.800000000000011" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="7"> <apply xmlns="http://schemas.mathsoft.com/math50"> <equal /> <apply> <integral /> <lambda> <boundVars> <id xml:space="preserve">x</id> </boundVars> <apply> <id xml:space="preserve">Δ</id> <id xml:space="preserve">x</id> </apply> </lambda> <lowerBound> <apply> <neg /> <id xml:space="preserve">∞</id> </apply> </lowerBound> <upperBound> <id xml:space="preserve">∞</id> </upperBound> </apply> <real>1</real> </apply> </math> </region>

• Δ(n, x) - 傳回狄喇克函數的 nth 導數，定義如下︰

<region id="ID0EYZ4BB" actualWidth="184.83833333333337" actualHeight="53.743333445231123" top="153.60000000000002" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="8">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">τ</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">Δ</id>
            <sequence>
              <id xml:space="preserve">n</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">τ</id>
            </sequence>
          </apply>
        </lambda>
        <degree>
          <placeholder />
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">Δ</id>
          <sequence>
            <apply>
              <plus />
              <id xml:space="preserve" labels="*">n</id>
              <real>1</real>
            </apply>
            <id xml:space="preserve" labels="VARIABLE">τ</id>
          </sequence>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

Δ(x) 與 Δ(n, x) 相關，如下所示︰

引數

• x 是實數純量。

• n 是非負整數。

相關主題

關於符號函數

範例︰狄喇克 (單位脈衝) 與 LambertW 函數

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