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pyplschmidt_d1.html
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pyplschmidt_d1.html
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
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<h1 id="plschmidt_d1">PlSchmidt_d1</h1>
<p>Compute all the Schmidt-normalized Legendre polynomials and first derivatives.</p>
<h1 id="usage">Usage</h1>
<p><code>p</code>, <code>dp</code> = pyshtools.PlSchmidt_d1 (<code>lmax</code>, <code>z</code>)</p>
<dl>
<dt><code>p</code> : float, dimension (<code>lmax</code>+1)</dt>
<dd>An array of Schmidt-normalized Legendre polynomials up to degree <code>lmax</code>. Degree <code>l</code> corresponds to array index <code>l</code>.
</dd>
<dt><code>dp</code> : float, dimension (<code>lmax</code>+1)</dt>
<dd>An array of the first derivatives of the Schmidt-normalized Legendre polynomials up to degree <code>lmax</code>. Degree <code>l</code> corresponds to array index <code>l</code>.
</dd>
</dl>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>lmax</code> :integer</dt>
<dd>The maximum degree of the Legendre polynomials to be computed.
</dd>
<dt><code>z</code> : float</dt>
<dd>The argument of the Legendre polynomial.
</dd>
</dl>
<h1 id="description">Description</h1>
<p><code>PlSchmidt_d1</code> will calculate all of the Schmidt-normalized Legendre polynomials and first derivatives up to degree <code>lmax</code> for a given argument. These are calculated using a standard three-term recursion formula, and the integral of the Schmidt-normalized Legendre polynomials over the interval [-1, 1] is <code>2/(2l+1)</code>. Note that the derivative of the Legendre polynomials is calculated with respect to its arguement <code>z</code>, and not latitude or colatitude. If <code>z=cos(theta)</code>, where <code>theta</code> is the colatitude, then it is only necessary to multiply <code>dp</code> by <code>-sin(theta)</code> to obtain the derivative with respect to <code>theta</code>.</p>
<h1 id="see-also">See also</h1>
<p><a href="pyplbar.html"><code>plbar</code></a>, <a href="pyplbar_d1.html"><code>plbar_d1</code></a>, <a href="pyplmbar.html"><code>plmbar</code></a>, <a href="pyplmbar_d1.html"><code>plmbar_d1</code></a>, <a href="pyplon.html"><code>plon</code></a>, <a href="pyplon_d1.html"><code>plon_d1</code></a>, <a href="pyplmon.html"><code>plmon</code></a>, <a href="pyplmon_d1.html"><code>plmon_d1</code></a>, <a href="pyplschmidt.html"><code>plschmidt</code></a>, <a href="pyplmschmidt.html"><code>plmschmidt</code></a>, <a href="pyplmschmidt_d1.html"><code>plmschmidt_d1</code></a>, <a href="pyplegendre.html"><code>plegendre</code></a>, <a href="pyplegendre_d1.html"><code>plegendre_d1</code></a>, <a href="pyplegendrea.html"><code>plegendrea</code></a>, <a href="pyplegendrea_d1.html"><code>plegendrea_d1</code></a></p>
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> <a href="../../../index.html" class="dir">Home</a> > <a href="../../documentation.html" class="dir">Documentation</a> > <a href="../../python-routines.html" class="dir">Python</a> > <a href="../../pylegendre.html" class="dir">Legendre Functions</a></p>
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