函數
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符號函數
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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="ID0EE5WIB" actualWidth="66.353333333333339" actualHeight="25.6" top="19.200000000000003" left="19.200000000000003" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="5" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <equal xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">Δ</id> <id xml:space="preserve" xml:lang="zh_TW">x</id> </apply> <real xml:lang="zh_TW">0</real> </apply> </math> </region>
if
<region id="ID0EL6WIB" actualWidth="37.176666666666662" actualHeight="25.6" top="19.200000000000003" left="230.40000000000003" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="6" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <notEqual xml:lang="zh_TW" /> <id xml:space="preserve" xml:lang="zh_TW">x</id> <real xml:lang="zh_TW">0</real> </apply> </math> </region>
以及
<region id="ID0ELBXIB" actualWidth="104.39833333333335" actualHeight="56.800000000000004" top="76.800000000000011" left="19.200000000000003" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="7" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <equal xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <integral xml:lang="zh_TW" /> <lambda xml:lang="zh_TW"> <boundVars xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">x</id> </boundVars> <apply xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">Δ</id> <id xml:space="preserve" xml:lang="zh_TW">x</id> </apply> </lambda> <lowerBound xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <neg xml:lang="zh_TW" /> <id xml:space="preserve" xml:lang="zh_TW">∞</id> </apply> </lowerBound> <upperBound xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">∞</id> </upperBound> </apply> <real xml:lang="zh_TW">1</real> </apply> </math> </region>
•
Δ(n, x)
- 傳回狄喇克函數的
n
th
導數，定義如下︰
<region id="ID0EAEXIB" actualWidth="184.83833333333337" actualHeight="53.743333445231123" top="153.60000000000002" left="19.200000000000003" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="8" xml:lang="zh_TW"> <symEval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <derivative xml:lang="zh_TW" /> <lambda xml:lang="zh_TW"> <boundVars xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">τ</id> </boundVars> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">Δ</id> <sequence xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">n</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">τ</id> </sequence> </apply> </lambda> <degree xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </degree> </apply> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW">Δ</id> <sequence xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <id labels="*" xml:space="preserve" xml:lang="zh_TW">n</id> <real xml:lang="zh_TW">1</real> </apply> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW">τ</id> </sequence> </apply> </symResult> </symEval> </math> </region>
Δ(x)
與
Δ(n, x)
相關，如下所示︰
<region id="ID0EBFXIB" actualWidth="109.92666666666668" actualHeight="25.6" top="230.40000000000003" left="19.200000000000003" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="9" xml:lang="zh_TW"> <apply xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <equal xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">Δ</id> <id xml:space="preserve" xml:lang="zh_TW">x</id> </apply> <apply xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW">Δ</id> <sequence xml:lang="zh_TW"> <real xml:lang="zh_TW">0</real> <id xml:space="preserve" xml:lang="zh_TW">x</id> </sequence> </apply> </apply> </math> </region>
引數
•
x
是實數純量。
•
n
是非負整數。
複製運算式
