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  <section id="legendre-series-numpy-polynomial-legendre">
<span id="module-numpy.polynomial.legendre"></span><h1>Legendre Series (<a class="reference internal" href="#module-numpy.polynomial.legendre" title="numpy.polynomial.legendre"><code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.polynomial.legendre</span></code></a>)<a class="headerlink" href="#legendre-series-numpy-polynomial-legendre" title="Link to this heading">#</a></h1>
<p>This module provides a number of objects (mostly functions) useful for
dealing with Legendre series, including a <a class="reference internal" href="generated/numpy.polynomial.legendre.Legendre.html#numpy.polynomial.legendre.Legendre" title="numpy.polynomial.legendre.Legendre"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Legendre</span></code></a> class that
encapsulates the usual arithmetic operations.  (General information
on how this module represents and works with such polynomials is in the
docstring for its “parent” sub-package, <a class="reference internal" href="routines.polynomials-package.html#module-numpy.polynomial" title="numpy.polynomial"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.polynomial</span></code></a>).</p>
<section id="classes">
<h2>Classes<a class="headerlink" href="#classes" title="Link to this heading">#</a></h2>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.Legendre.html#numpy.polynomial.legendre.Legendre" title="numpy.polynomial.legendre.Legendre"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Legendre</span></code></a>(coef[, domain, window, symbol])</p></td>
<td><p>A Legendre series class.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="constants">
<h2>Constants<a class="headerlink" href="#constants" title="Link to this heading">#</a></h2>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legdomain.html#numpy.polynomial.legendre.legdomain" title="numpy.polynomial.legendre.legdomain"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legdomain</span></code></a></p></td>
<td><p>An array object represents a multidimensional, homogeneous array of fixed-size items.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legzero.html#numpy.polynomial.legendre.legzero" title="numpy.polynomial.legendre.legzero"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legzero</span></code></a></p></td>
<td><p>An array object represents a multidimensional, homogeneous array of fixed-size items.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legone.html#numpy.polynomial.legendre.legone" title="numpy.polynomial.legendre.legone"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legone</span></code></a></p></td>
<td><p>An array object represents a multidimensional, homogeneous array of fixed-size items.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legx.html#numpy.polynomial.legendre.legx" title="numpy.polynomial.legendre.legx"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legx</span></code></a></p></td>
<td><p>An array object represents a multidimensional, homogeneous array of fixed-size items.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="arithmetic">
<h2>Arithmetic<a class="headerlink" href="#arithmetic" title="Link to this heading">#</a></h2>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legadd.html#numpy.polynomial.legendre.legadd" title="numpy.polynomial.legendre.legadd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legadd</span></code></a>(c1, c2)</p></td>
<td><p>Add one Legendre series to another.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legsub.html#numpy.polynomial.legendre.legsub" title="numpy.polynomial.legendre.legsub"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legsub</span></code></a>(c1, c2)</p></td>
<td><p>Subtract one Legendre series from another.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legmulx.html#numpy.polynomial.legendre.legmulx" title="numpy.polynomial.legendre.legmulx"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legmulx</span></code></a>(c)</p></td>
<td><p>Multiply a Legendre series by x.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legmul.html#numpy.polynomial.legendre.legmul" title="numpy.polynomial.legendre.legmul"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legmul</span></code></a>(c1, c2)</p></td>
<td><p>Multiply one Legendre series by another.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legdiv.html#numpy.polynomial.legendre.legdiv" title="numpy.polynomial.legendre.legdiv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legdiv</span></code></a>(c1, c2)</p></td>
<td><p>Divide one Legendre series by another.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legpow.html#numpy.polynomial.legendre.legpow" title="numpy.polynomial.legendre.legpow"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legpow</span></code></a>(c, pow[, maxpower])</p></td>
<td><p>Raise a Legendre series to a power.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legval.html#numpy.polynomial.legendre.legval" title="numpy.polynomial.legendre.legval"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legval</span></code></a>(x, c[, tensor])</p></td>
<td><p>Evaluate a Legendre series at points x.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legval2d.html#numpy.polynomial.legendre.legval2d" title="numpy.polynomial.legendre.legval2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legval2d</span></code></a>(x, y, c)</p></td>
<td><p>Evaluate a 2-D Legendre series at points (x, y).</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legval3d.html#numpy.polynomial.legendre.legval3d" title="numpy.polynomial.legendre.legval3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legval3d</span></code></a>(x, y, z, c)</p></td>
<td><p>Evaluate a 3-D Legendre series at points (x, y, z).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.leggrid2d.html#numpy.polynomial.legendre.leggrid2d" title="numpy.polynomial.legendre.leggrid2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">leggrid2d</span></code></a>(x, y, c)</p></td>
<td><p>Evaluate a 2-D Legendre series on the Cartesian product of x and y.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.leggrid3d.html#numpy.polynomial.legendre.leggrid3d" title="numpy.polynomial.legendre.leggrid3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">leggrid3d</span></code></a>(x, y, z, c)</p></td>
<td><p>Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="calculus">
<h2>Calculus<a class="headerlink" href="#calculus" title="Link to this heading">#</a></h2>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legder.html#numpy.polynomial.legendre.legder" title="numpy.polynomial.legendre.legder"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legder</span></code></a>(c[, m, scl, axis])</p></td>
<td><p>Differentiate a Legendre series.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legint.html#numpy.polynomial.legendre.legint" title="numpy.polynomial.legendre.legint"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legint</span></code></a>(c[, m, k, lbnd, scl, axis])</p></td>
<td><p>Integrate a Legendre series.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="misc-functions">
<h2>Misc Functions<a class="headerlink" href="#misc-functions" title="Link to this heading">#</a></h2>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legfromroots.html#numpy.polynomial.legendre.legfromroots" title="numpy.polynomial.legendre.legfromroots"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legfromroots</span></code></a>(roots)</p></td>
<td><p>Generate a Legendre series with given roots.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legroots.html#numpy.polynomial.legendre.legroots" title="numpy.polynomial.legendre.legroots"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legroots</span></code></a>(c)</p></td>
<td><p>Compute the roots of a Legendre series.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legvander.html#numpy.polynomial.legendre.legvander" title="numpy.polynomial.legendre.legvander"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legvander</span></code></a>(x, deg)</p></td>
<td><p>Pseudo-Vandermonde matrix of given degree.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legvander2d.html#numpy.polynomial.legendre.legvander2d" title="numpy.polynomial.legendre.legvander2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legvander2d</span></code></a>(x, y, deg)</p></td>
<td><p>Pseudo-Vandermonde matrix of given degrees.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legvander3d.html#numpy.polynomial.legendre.legvander3d" title="numpy.polynomial.legendre.legvander3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legvander3d</span></code></a>(x, y, z, deg)</p></td>
<td><p>Pseudo-Vandermonde matrix of given degrees.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.leggauss.html#numpy.polynomial.legendre.leggauss" title="numpy.polynomial.legendre.leggauss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">leggauss</span></code></a>(deg)</p></td>
<td><p>Gauss-Legendre quadrature.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legweight.html#numpy.polynomial.legendre.legweight" title="numpy.polynomial.legendre.legweight"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legweight</span></code></a>(x)</p></td>
<td><p>Weight function of the Legendre polynomials.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legcompanion.html#numpy.polynomial.legendre.legcompanion" title="numpy.polynomial.legendre.legcompanion"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legcompanion</span></code></a>(c)</p></td>
<td><p>Return the scaled companion matrix of c.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legfit.html#numpy.polynomial.legendre.legfit" title="numpy.polynomial.legendre.legfit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legfit</span></code></a>(x, y, deg[, rcond, full, w])</p></td>
<td><p>Least squares fit of Legendre series to data.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legtrim.html#numpy.polynomial.legendre.legtrim" title="numpy.polynomial.legendre.legtrim"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legtrim</span></code></a>(c[, tol])</p></td>
<td><p>Remove &quot;small&quot; &quot;trailing&quot; coefficients from a polynomial.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.legline.html#numpy.polynomial.legendre.legline" title="numpy.polynomial.legendre.legline"><code class="xref py py-obj docutils literal notranslate"><span class="pre">legline</span></code></a>(off, scl)</p></td>
<td><p>Legendre series whose graph is a straight line.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.leg2poly.html#numpy.polynomial.legendre.leg2poly" title="numpy.polynomial.legendre.leg2poly"><code class="xref py py-obj docutils literal notranslate"><span class="pre">leg2poly</span></code></a>(c)</p></td>
<td><p>Convert a Legendre series to a polynomial.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.legendre.poly2leg.html#numpy.polynomial.legendre.poly2leg" title="numpy.polynomial.legendre.poly2leg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">poly2leg</span></code></a>(pol)</p></td>
<td><p>Convert a polynomial to a Legendre series.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="see-also">
<h2>See also<a class="headerlink" href="#see-also" title="Link to this heading">#</a></h2>
<p>numpy.polynomial</p>
</section>
</section>


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