Esempio: funzioni delta di Dirac (impulso di Dirac) e di LambertW

Funzioni > Funzioni simboliche > Esempio: funzioni delta di Dirac (impulso di Dirac) e di LambertW

In questo esempio vengono fornite informazioni sulla funzione delta di Dirac e sulle proprietà della funzione LambertW.

Funzione delta di Dirac

Le proprietà della funzione delta di Dirac sono le seguenti:

Le trasformate seguenti restituiscono i risultati secondo la funzione delta di Dirac:

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      <apply>
        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">Φ</id>
        <id xml:space="preserve">τ</id>
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          <id xml:space="preserve">fourier</id>
          <id xml:space="preserve">τ</id>
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        <apply>
          <div />
          <apply>
            <plus />
            <apply>
              <mult />
              <apply>
                <mult />
                <id xml:space="preserve" labels="*">ω</id>
                <id xml:space="preserve" labels="CONSTANT">π</id>
              </apply>
              <apply>
                <id xml:space="preserve" labels="FUNCTION">Δ</id>
                <id xml:space="preserve" labels="*">ω</id>
              </apply>
            </apply>
            <imag symbol="i">1</imag>
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          <id xml:space="preserve" labels="*">ω</id>
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Nell'esempio precedente, Φ è la funzione a gradino di Heaviside.

Funzione LambertW

La funzione LambertW compare nella soluzione simbolica delle equazioni seguenti:

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        <equal />
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            <pow />
            <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
            <id xml:space="preserve">u</id>
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        <real>0</real>
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      <command>
        <sequence>
          <id xml:space="preserve">solve</id>
          <id xml:space="preserve">u</id>
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      <symResult>
        <apply>
          <neg />
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            <id xml:space="preserve" labels="*">LambertW</id>
            <apply>
              <neg />
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                <real>1</real>
                <real>5</real>
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                <id xml:space="preserve" labels="*">LambertW</id>
                <apply>
                  <div />
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Queste sono l'integrale, la derivata e l'espansione di una serie di Taylor della funzione LambertW:

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                <id xml:space="preserve" labels="VARIABLE">x</id>
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                  <id xml:space="preserve" labels="VARIABLE">x</id>
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