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<a href="#func-members">Functions/Subroutines</a> </div>
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<div class="title">coeff Module Reference</div> </div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions/Subroutines</h2></td></tr>
<tr class="memitem:adab57f8a534960ecfe42f7f37133d15a"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#adab57f8a534960ecfe42f7f37133d15a">ALLX2L</a> (n, k, s, m)</td></tr>
<tr class="memdesc:adab57f8a534960ecfe42f7f37133d15a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the associated-Laguerre/Laguerre/x to Laguerre basis transformation coefficient <img class="formulaInl" alt="$ d^{|m|}_{nks} $" src="form_4.png"/>,. <a href="#adab57f8a534960ecfe42f7f37133d15a">More...</a><br /></td></tr>
<tr class="separator:adab57f8a534960ecfe42f7f37133d15a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9cb6583d869a3fc9fb50b015d84d29fd"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a9cb6583d869a3fc9fb50b015d84d29fd">ALL2L</a> (n, k, s, m)</td></tr>
<tr class="memdesc:a9cb6583d869a3fc9fb50b015d84d29fd"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the associated-Laguerre/Laguerre to Laguerre basis transformation coefficient <img class="formulaInl" alt="$ \overline{d}^{|m|}_{nkf} $" src="form_7.png"/>,. <a href="#a9cb6583d869a3fc9fb50b015d84d29fd">More...</a><br /></td></tr>
<tr class="separator:a9cb6583d869a3fc9fb50b015d84d29fd"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a48c8c2f0290d8906c6ac9186188472e2"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a48c8c2f0290d8906c6ac9186188472e2">Lpjl</a> (p, j, l)</td></tr>
<tr class="memdesc:a48c8c2f0290d8906c6ac9186188472e2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the associated Laguerre serie coefficient <img class="formulaInl" alt="$ L_{jl}^p $" src="form_9.png"/>. <a href="#a48c8c2f0290d8906c6ac9186188472e2">More...</a><br /></td></tr>
<tr class="separator:a48c8c2f0290d8906c6ac9186188472e2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1b8a67479172d76c53247c29af0f8e5d"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a1b8a67479172d76c53247c29af0f8e5d">curlyAmn</a> (m, n, ba)</td></tr>
<tr class="memdesc:a1b8a67479172d76c53247c29af0f8e5d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the particle species 'a' FLR coefficients. <a href="#a1b8a67479172d76c53247c29af0f8e5d">More...</a><br /></td></tr>
<tr class="separator:a1b8a67479172d76c53247c29af0f8e5d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a418b3417e66bba09cfe9dea26b7aa19a"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a418b3417e66bba09cfe9dea26b7aa19a">curlyBmn</a> (m, n, b_)</td></tr>
<tr class="memdesc:a418b3417e66bba09cfe9dea26b7aa19a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the particle species 'b' FLR coefficients. <a href="#a418b3417e66bba09cfe9dea26b7aa19a">More...</a><br /></td></tr>
<tr class="separator:a418b3417e66bba09cfe9dea26b7aa19a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a70b8fda4de135db12f9748044ca991f9"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a70b8fda4de135db12f9748044ca991f9">kerneln</a> (b, n)</td></tr>
<tr class="memdesc:a70b8fda4de135db12f9748044ca991f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the nth-order kernel function. <a href="#a70b8fda4de135db12f9748044ca991f9">More...</a><br /></td></tr>
<tr class="separator:a70b8fda4de135db12f9748044ca991f9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a02da72ff61eb840d9ec2e640e151fefd"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a02da72ff61eb840d9ec2e640e151fefd">normepm</a> (p, m)</td></tr>
<tr class="separator:a02da72ff61eb840d9ec2e640e151fefd"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a35ececef124d8a2863dd0af895b73646"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a35ececef124d8a2863dd0af895b73646">Injlkmp</a> (n, j, l, k, m, p)</td></tr>
<tr class="separator:a35ececef124d8a2863dd0af895b73646"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8057226d532cb6772dee7c246ae80e2a"><td class="memItemLeft" align="right" valign="top">type(fm) function, public&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecoeff.html#a8057226d532cb6772dee7c246ae80e2a">sigmapj</a> (p, j)</td></tr>
<tr class="memdesc:a8057226d532cb6772dee7c246ae80e2a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the spherical harmonics normalization coefficient. <a href="#a8057226d532cb6772dee7c246ae80e2a">More...</a><br /></td></tr>
<tr class="separator:a8057226d532cb6772dee7c246ae80e2a"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<h2 class="groupheader">Function/Subroutine Documentation</h2>
<a class="anchor" id="a9cb6583d869a3fc9fb50b015d84d29fd"></a>
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<td class="memname">type(fm) function, public coeff::ALL2L </td>
<td>(</td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>k</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>s</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>m</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Computes the associated-Laguerre/Laguerre to Laguerre basis transformation coefficient <img class="formulaInl" alt="$ \overline{d}^{|m|}_{nkf} $" src="form_7.png"/>,. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \overline{d}^{|m|}_{nkf} = \sum_{n_1 = 0}^n \sum_{k_1 =0}^k \sum_{f_1=0}^f L_{kk_1}^{-1/2} L_{nn_1}^{|m|-1/2} L_{f f_1}^{-1/2} (n_1 + k_1 + f_1)!. \]" src="form_8.png"/>
</p>
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000001">Todo:</a></b></dt><dd>Checked against Mathematica </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td></td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">k</td><td></td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">s</td><td></td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">m</td><td></td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">XOUT</td><td></td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="adab57f8a534960ecfe42f7f37133d15a"></a>
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<td class="memname">type(fm) function, public coeff::ALLX2L </td>
<td>(</td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>k</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>s</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>m</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Computes the associated-Laguerre/Laguerre/x to Laguerre basis transformation coefficient <img class="formulaInl" alt="$ d^{|m|}_{nks} $" src="form_4.png"/>,. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ L_n^{|m|}(x) L_k(x) x^{|m|} =\sum_{s=0}^{n+|m| +k} d^{|m|}_{nks} L_s(x),\]" src="form_2.png"/>
</p>
<p> where </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[d^{|m|}_{nks} = \int_0^\infty d x e^{-x} L_n^{|m|}(x) L_s(x) L_k(x) x^{|m|}. \]" src="form_3.png"/>
</p>
<p> yielding the closed analyticalform, </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ d_{nks}^{|m|} =\sum_{n_1=0}^{n} \sum_{k_1=0}^k \sum_{s_1=0}^s L_{kk_1}^{-1/2} L_{nn_1}^{|m|-1/2} L_{ss_1}^{-1/2} (n_1 + k_1 + s_1 + |m|)!, \]" src="form_5.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td></td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">k</td><td></td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">s</td><td></td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">m</td><td></td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">XOUT</td><td>Output result </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a1b8a67479172d76c53247c29af0f8e5d"></a>
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<td class="memname">type(fm) function, public coeff::curlyAmn </td>
<td>(</td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">type(fm), intent(in)&#160;</td>
<td class="paramname"><em>ba</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Computes the particle species 'a' FLR coefficients. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathcal{A}_{an}^m = \frac{ \sigma_m n!}{(n+|m|)!}\left(\frac{b_a}{2} \right)^{|m|} \mathcal{K}_{n}(b_a) \]" src="form_16.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">m</td><td>Spherical Harmonics order </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>FLR order </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">ba</td><td>Thermal Normalized Perpendicular Wavenumber </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">Amn</td><td></td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a418b3417e66bba09cfe9dea26b7aa19a"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">type(fm) function, public coeff::curlyBmn </td>
<td>(</td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">type(fm), intent(in)&#160;</td>
<td class="paramname"><em>b_</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Computes the particle species 'b' FLR coefficients. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">m</td><td>Spherical Harmonics order </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>FLR order </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">bb</td><td>Thermal Normalized Perpendicular Wavenumber </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">Bmn</td><td></td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a35ececef124d8a2863dd0af895b73646"></a>
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<td class="memname">type(fm) function, public coeff::Injlkmp </td>
<td>(</td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>j</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>l</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>k</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>p</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
</div>
</div>
<a class="anchor" id="a70b8fda4de135db12f9748044ca991f9"></a>
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<td class="memname">type(fm) function, public coeff::kerneln </td>
<td>(</td>
<td class="paramtype">type(fm), intent(in)&#160;</td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Computes the nth-order kernel function. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathcal{K}_n(x) = \frac{1}{n!} \left(\frac{x}{2} \right)^{2n } e^{- x^2/4} \]" src="form_17.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>kernel order </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">b</td><td>normalized perpendicular wavevector </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">kerneln</td><td></td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a48c8c2f0290d8906c6ac9186188472e2"></a>
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<div class="memproto">
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<td class="memname">type(fm) function, public coeff::Lpjl </td>
<td>(</td>
<td class="paramtype">real(dp), intent(in)&#160;</td>
<td class="paramname"><em>p</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">real(dp), intent(in)&#160;</td>
<td class="paramname"><em>j</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">real(dp), intent(in)&#160;</td>
<td class="paramname"><em>l</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Computes the associated Laguerre serie coefficient <img class="formulaInl" alt="$ L_{jl}^p $" src="form_9.png"/>. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ L_{jl}^{p} = \frac{(-1)^l (p + j + 1/2)!}{(j - l)!(l +p + 1/2 )! l!}. \]" src="form_10.png"/>
</p>
<p> such that </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ L^{p+1/2}_j(x) = \sum_{l=0}^p L_{jl}^p L_l(x) \]" src="form_13.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">XOUT</td><td></td></tr>
</table>
</dd>
</dl>
</div>
</div>
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<td class="memname">type(fm) function, public coeff::normepm </td>
<td>(</td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>p</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>m</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<td class="memname">type(fm) function, public coeff::sigmapj </td>
<td>(</td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>p</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">integer, intent(in)&#160;</td>
<td class="paramname"><em>j</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<p>Computes the spherical harmonics normalization coefficient. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \]" src="form_33.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">p</td><td></td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">j</td><td></td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">Results</td><td></td></tr>
</table>
</dd>
</dl>
</div>
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