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paulmasson committed Mar 14, 2024
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2 changes: 1 addition & 1 deletion docs/functions/am.html
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<p>The Jacobi amplitude function of <i>z</i> and parameter <i>m</i> in Math. Defined as the inverse of the incomplete elliptic integral of the first kind:</p>

\[ u = \int_0^\phi \frac{ d \theta }{ \sqrt{ 1 - m \sin^2 \theta } } \qquad \rightarrow \qquad \operatorname{am}( u | m ) = \phi \]
\[ z = \int_0^\phi \frac{ d \theta }{ \sqrt{ 1 - m \sin^2 \theta } } \qquad \rightarrow \qquad \operatorname{am}( z | m ) = \phi \]

<p>Note that all Jacobi elliptic functions in Math use the parameter rather than the elliptic modulus <i>k</i>, which is related to the parameter by \( m = k^2 \).</p>

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2 changes: 1 addition & 1 deletion docs/functions/cn.html
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<p>The Jacobi elliptic cosine function of <i>z</i> and parameter <i>m</i> in Math. Defined as the cosine of the Jacobi amplitude:</p>

\[ \operatorname{cn}( u | m ) = \cos [ \operatorname{am}( u | m ) ] \]
\[ \operatorname{cn}( z | m ) = \cos [ \operatorname{am}( z | m ) ] \]

<p>Note that all Jacobi elliptic functions in Math use the parameter rather than the elliptic modulus <i>k</i>, which is related to the parameter by \( m = k^2 \).</p>

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2 changes: 1 addition & 1 deletion docs/functions/dn.html
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<p>The Jacobi delta amplitude function of <i>z</i> and parameter <i>m</i> in Math. Defined by</p>

\[ \operatorname{dn}( u | m ) = \sqrt{ 1 - m \operatorname{sn}^2( u | m ) } \]
\[ \operatorname{dn}( z | m ) = \sqrt{ 1 - m \operatorname{sn}^2( z| m ) } \]

<p>Note that all Jacobi elliptic functions in Math use the parameter rather than the elliptic modulus <i>k</i>, which is related to the parameter by \( m = k^2 \).</p>

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2 changes: 1 addition & 1 deletion docs/functions/sn.html
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<p>The Jacobi elliptic sine function of <i>z</i> and parameter <i>m</i> in Math. Defined as the sine of the Jacobi amplitude:</p>

\[ \operatorname{sn}( u | m ) = \sin [ \operatorname{am}( u | m ) ] \]
\[ \operatorname{sn}( z | m ) = \sin [ \operatorname{am}( z | m ) ] \]

<p>Note that all Jacobi elliptic functions in Math use the parameter rather than the elliptic modulus <i>k</i>, which is related to the parameter by \( m = k^2 \).</p>

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