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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>call PlSchmidt_d1 (<code>p</code>, <code>dp</code>, <code>lmax</code>, <code>z</code>, <code>exitstatus</code>)</p>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>p</code> : output, real*8, 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+1</code>.
</dd>
<dt><code>dp</code> : output, real*8, 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+1</code>.
</dd>
<dt><code>lmax</code> : input, integer</dt>
<dd>The maximum degree of the Legendre polynomials to be computed.
</dd>
<dt><code>z</code> : input, real*8</dt>
<dd>The argument of the Legendre polynomial.
</dd>
<dt><code>exitstatus</code> : output, optional, integer</dt>
<dd>If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.
</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="plbar.html"><code>plbar</code></a>, <a href="plbar_d1.html"><code>plbar_d1</code></a>, <a href="plmbar.html"><code>plmbar</code></a>, <a href="plmbar_d1.html"><code>plmbar_d1</code></a>, <a href="plon.html"><code>plon</code></a>, <a href="plon_d1.html"><code>plon_d1</code></a>, <a href="plmon.html"><code>plmon</code></a>, <a href="plmon_d1.html"><code>plmon_d1</code></a>, <a href="plschmidt.html"><code>plschmidt</code></a>, <a href="plmschmidt.html"><code>plmschmidt</code></a>, <a href="plmschmidt_d1.html"><code>plmschmidt_d1</code></a>, <a href="plegendre.html"><code>plegendre</code></a>, <a href="plegendre_d1.html"><code>plegendre_d1</code></a>, <a href="plegendrea.html"><code>plegendrea</code></a>, <a href="plegendrea_d1.html"><code>plegendrea_d1</code></a></p>
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