Ejemplo: funciones modificadas de Bessel de primera especie

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Muestre la relación entre las funciones I0, I1 e In. Muestre también las relaciones entre estas funciones y sus versiones escaladas.

1. Defina dos variables de rango de paso:

2. Trace las funciones I0 y I1. Añada la función de segundo orden In al gráfico:

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                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
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                  <id labels="FUNCTION" xml:space="preserve">I1</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <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. Trace la función de quinto y octavo orden In:

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                  <id labels="FUNCTION" xml:space="preserve">I0</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
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              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">I1</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <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>
                  </sequence>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id labels="FUNCTION" xml:space="preserve">In</id>
                  <sequence>
                    <apply>
                      <plus />
                      <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">m</id>
                      <real>3</real>
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                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                  </sequence>
                </apply>
              </math>
              <math>
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            <plotEquation>
              <math>
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                  <id labels="FUNCTION" xml:space="preserve">In</id>
                  <sequence>
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                      <plus />
                      <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">m</id>
                      <real>6</real>
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                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
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• Cuanto más alto sea el orden de la función In, más brusca será la transición desde cero.

• Solo la función I0 tiene su origen en (x=0,y=1). El resto de órdenes tienen su origen en (x=0,y=0)..

4. Cree un gráfico para mostrar que I0(y)=In(0,y). Redefina los valores de marca de graduación para ampliar el eje X con el fin de mostrar más detalles:

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            <gridLabels display="true" />
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            <plotEquation>
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                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">y</id>
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5. Cree un gráfico para mostrar que I1(y)=In(1,y). Redefina los valores de marca de graduación para ampliar el eje X con el fin de mostrar más detalles:

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6. Utilice la evaluación simbólica para mostrar la relación entre cada función y su versión escalada:

7. Utilice un gráfico para mostrar que:

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Las funciones modificadas de Bessel de primera especie no tienen picos.

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