Esempio: Confronto tra le funzioni simboliche Hypergeom, Mhyper e Fhyper

Funzioni > Funzioni simboliche > Esempio: Confronto tra le funzioni simboliche Hypergeom, Mhyper e Fhyper

Funzione hypergeom

1. L'integrale riportato di seguito è definito in termini della funzione hypergeom come descritto di seguito:

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    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <integral />
        <lambda>
          <boundVars>
            <id xml:space="preserve">x</id>
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          <apply>
            <div />
            <real>1</real>
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        <lowerBound>
          <placeholder />
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        <id xml:space="preserve" labels="FUNCTION">x</id>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">hypergeom</id>
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            <matrix rows="2" cols="1">
              <apply>
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                <real>1</real>
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                  <real>1</real>
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              <neg />
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                <id xml:space="preserve">n</id>
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2. Valutare il risultato alle estremità dell'intervallo [1, 2].

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      <apply>
        <minus />
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          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">b</id>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">hypergeom</id>
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                  <real>1</real>
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                <real>1</real>
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              <matrix rows="1" cols="1">
                <apply>
                  <div />
                  <apply>
                    <plus />
                    <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</id>
                    <real>1</real>
                  </apply>
                  <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</id>
                </apply>
              </matrix>
              <apply>
                <neg />
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">b</id>
                  <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</id>
                </apply>
              </apply>
            </sequence>
          </apply>
        </apply>
        <apply>
          <mult />
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">a</id>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">hypergeom</id>
            <sequence>
              <matrix rows="2" cols="1">
                <apply>
                  <div />
                  <real>1</real>
                  <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</id>
                </apply>
                <real>1</real>
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              <matrix rows="1" cols="1">
                <apply>
                  <div />
                  <apply>
                    <plus />
                    <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</id>
                    <real>1</real>
                  </apply>
                  <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</id>
                </apply>
              </matrix>
              <apply>
                <neg />
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">a</id>
                  <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</id>
                </apply>
              </apply>
            </sequence>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">float</id>
          <real>14</real>
        </sequence>
      </command>
      <symResult>
        <real>0.10040640511009</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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3. Verificare che il risultato numerico precedente corrisponda al valore dell'integrale definito equivalente.

Funzione mhyper

1. Assegnare valori ai parametri della funzione mhyper.

2. Valutare la funzione per mhyper(a,b,x).

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        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">mhyper</id>
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          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">b</id>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
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3. Verificare che la funzione hypergeom restituisca gli stessi risultati di mhyper per il caso speciale in cui:

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">hypergeom</id>
        <sequence>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n1</id>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">d</id>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
        </sequence>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">float</id>
          <real>15</real>
        </sequence>
      </command>
      <symResult>
        <real>1.29744254140026</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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Funzione fhyper

1. Assegnare valori ai parametri della funzione fhyper.

2. Valutare la funzione per fhyper(a,b,c,x).

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        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">fhyper</id>
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          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">a</id>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">b</id>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">c</id>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
        </sequence>
      </apply>
      <unitOverride>
        <placeholder />
      </unitOverride>
    </eval>
    <resultFormat>
      <general precision="15" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
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3. Verificare che la funzione hypergeom restituisca gli stessi risultati di fhyper per il caso speciale in cui:

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        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">hypergeom</id>
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          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">d</id>
          <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">x</id>
        </sequence>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">float</id>
          <real>15</real>
        </sequence>
      </command>
      <symResult>
        <real>1.54517744447956</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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