update docs and readme

README.md

@@ -1,6 +1,6 @@
 # orthopoly
 
-This is a package for using sets of orthogonal functions/polynomials. Currently, it includes the [Chebyshev polynomials](http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html) and the [spherical harmonics](http://mathworld.wolfram.com/SphericalHarmonic.html). The package is MIT licensed. Use it almost however you like. **Documentation** is available here: [https://wordsworthgroup.github.io/orthopoly](https://wordsworthgroup.github.io/orthopoly)
+This is a package for using sets of orthogonal functions/polynomials. Currently, it includes Chebyshev, Legendre, and Gegenbauer polynomials. It also has real, two-dimensional spherical harmonics. It's MIT licensed. Use it almost however you like. **Documentation** is available here: [https://wordsworthgroup.github.io/orthopoly](https://wordsworthgroup.github.io/orthopoly)
 
 ### Installing/Using
 
@@ -33,7 +33,7 @@ This module implements the Associated Legendre Polynomials and their first two d
 
 ### spherical_harmonic
 
-The `spherical_harmonic` module provides functions for evaluating the real, two-dimensional (surface), orthonormal, spherical harmonics. It contains functions for evaluating the associated Legendre polynomials and their first two derivatives via stable recursion relationships. From the associated Legendre polynomials, the spherical harmonics, their gradients, and their Laplacians can be evaluated. The module also contains some functions for creating grids on the sphere (regular, icosahedral, and Fibonacci) and for creating random spherical harmonic expansions with specific power density relationships (noise). The module does not have functions for performing spherical harmonic analysis (transforming from values on the sphere to expansion coefficients).
+The `spherical_harmonic` module provides functions for evaluating the real, two-dimensional (surface), orthonormal, spherical harmonics.  From the associated Legendre polynomials, the spherical harmonics, their gradients, and their Laplacians can be evaluated. The module also contains some functions for creating grids on the sphere (regular, icosahedral, and Fibonacci) and for creating random spherical harmonic expansions with specific power density relationships (noise). The module does not have functions for performing spherical harmonic analysis (transforming from values on the sphere to expansion coefficients).
 
 For some applications, fitting a spherical harmonic expansion to data in spherical coordinates is useful. A least squares fit can be computed with the pseudoinverse of a matrix full of spherical harmonic function evaluations (see `sph_har_matrix` and related functions). However, this should only be done when the number of points is much greater than the number of terms in the fitted expansion.
 

docs/index.html

@@ -35,7 +35,7 @@
   <img alt="_images/orthopoly.png" src="_images/orthopoly.png" />
 <div class="section" id="module-orthopoly">
 <span id="welcome-to-orthopoly-s-documentation"></span><h1>Welcome to orthopoly’s documentation!<a class="headerlink" href="#module-orthopoly" title="Permalink to this headline">¶</a></h1>
-<p>This is a package for using sets of orthogonal functions/polynomials. Currently, it includes the Chebyshev polynomials and the spherical harmonics. It’s MIT licensed. Use it almost however you like.</p>
+<p>This is a package for using sets of orthogonal functions/polynomials. Currently, it includes Chebyshev, Legendre, and Gegenbauer polynomials. It also has real, two-dimensional spherical harmonics. It’s MIT licensed. Use it almost however you like.</p>
 <div class="section" id="installing-using">
 <h2>Installing/Using<a class="headerlink" href="#installing-using" title="Permalink to this headline">¶</a></h2>
 <p>To install the package, you can</p>
@@ -65,7 +65,7 @@ <h2>legendre<a class="headerlink" href="#legendre" title="Permalink to this head
 </div>
 <div class="section" id="spherical-harmonic">
 <h2>spherical_harmonic<a class="headerlink" href="#spherical-harmonic" title="Permalink to this headline">¶</a></h2>
-<p>The <a class="reference internal" href="spherical_harmonic.html#module-orthopoly.spherical_harmonic" title="orthopoly.spherical_harmonic"><code class="xref py py-mod docutils literal notranslate"><span class="pre">spherical_harmonic</span></code></a> module provides functions for evaluating the real, two-dimensional (surface), orthonormal, spherical harmonics. It contains functions for evaluating the associated Legendre polynomials and their first two derivatives via stable recursion relationships. From the associated Legendre polynomials, the <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.sph_har" title="orthopoly.spherical_harmonic.sph_har"><code class="xref py py-func docutils literal notranslate"><span class="pre">spherical</span> <span class="pre">harmonics</span></code></a>, their <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grad_sph_har" title="orthopoly.spherical_harmonic.grad_sph_har"><code class="xref py py-func docutils literal notranslate"><span class="pre">gradients</span></code></a>, and their <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.lap_sph_har" title="orthopoly.spherical_harmonic.lap_sph_har"><code class="xref py py-func docutils literal notranslate"><span class="pre">Laplacians</span></code></a> can be evaluated. The module also contains some functions for creating grids on the sphere (<a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grid_regular" title="orthopoly.spherical_harmonic.grid_regular"><code class="xref py py-func docutils literal notranslate"><span class="pre">regular</span></code></a>, <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grid_icosahedral" title="orthopoly.spherical_harmonic.grid_icosahedral"><code class="xref py py-func docutils literal notranslate"><span class="pre">icosahedral</span></code></a>, and <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grid_fibonacci" title="orthopoly.spherical_harmonic.grid_fibonacci"><code class="xref py py-func docutils literal notranslate"><span class="pre">Fibonacci</span></code></a>) and for creating random spherical harmonic expansions with specific power density relationships (noise). The module does not have functions for performing spherical harmonic analysis (transforming from values on the sphere to expansion coefficients).</p>
+<p>The <a class="reference internal" href="spherical_harmonic.html#module-orthopoly.spherical_harmonic" title="orthopoly.spherical_harmonic"><code class="xref py py-mod docutils literal notranslate"><span class="pre">spherical_harmonic</span></code></a> module provides functions for evaluating the real, two-dimensional (surface), orthonormal, spherical harmonics. From the associated Legendre polynomials, the <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.sph_har" title="orthopoly.spherical_harmonic.sph_har"><code class="xref py py-func docutils literal notranslate"><span class="pre">spherical</span> <span class="pre">harmonics</span></code></a>, their <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grad_sph_har" title="orthopoly.spherical_harmonic.grad_sph_har"><code class="xref py py-func docutils literal notranslate"><span class="pre">gradients</span></code></a>, and their <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.lap_sph_har" title="orthopoly.spherical_harmonic.lap_sph_har"><code class="xref py py-func docutils literal notranslate"><span class="pre">Laplacians</span></code></a> can be evaluated. The module also contains some functions for creating grids on the sphere (<a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grid_regular" title="orthopoly.spherical_harmonic.grid_regular"><code class="xref py py-func docutils literal notranslate"><span class="pre">regular</span></code></a>, <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grid_icosahedral" title="orthopoly.spherical_harmonic.grid_icosahedral"><code class="xref py py-func docutils literal notranslate"><span class="pre">icosahedral</span></code></a>, and <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.grid_fibonacci" title="orthopoly.spherical_harmonic.grid_fibonacci"><code class="xref py py-func docutils literal notranslate"><span class="pre">Fibonacci</span></code></a>) and for creating random spherical harmonic expansions with specific power density relationships (noise). The module does not have functions for performing spherical harmonic analysis (transforming from values on the sphere to expansion coefficients).</p>
 <p>For some applications, fitting a spherical harmonic expansion to data in spherical coordinates is useful. A least squares fit can be computed with the pseudoinverse of a matrix full of spherical harmonic function evaluations (see <a class="reference internal" href="spherical_harmonic.html#orthopoly.spherical_harmonic.sph_har_matrix" title="orthopoly.spherical_harmonic.sph_har_matrix"><code class="xref py py-func docutils literal notranslate"><span class="pre">sph_har_matrix</span></code></a> and related functions). However, this should only be done when the number of points is much greater than the number of terms in the fitted expansion.</p>
 <p>The books cited above have some good discussion of spherical harmonics. Other useful sources include:</p>
 <ul class="simple">