Editing Appendix/Ramblings/CCGF (section)

==Preface by Tohline==
[http://adsabs.harvard.edu/abs/1999ApJ...527...86C Cohl &amp; Tohline (1999)] present an expression for the Newtonian gravitational potential in terms of a ''Compact Cylindrical Green's Function'' expansion.  Over a professional career that dates back to 1976, this has turned out to be one of my most oft-cited research publications and ''certainly'' has proven to be the publication with the most citations from research groups outside of the astrophysics community.  A [[Appendix/Ramblings/CCGF#Sample_Citations_from_Fields_Outside_of_Astronomy|sample of citations from outside the field of astronomy]] is presented, below.  [http://hcohl.sdf.org/bibliography.html Howard Cohl] deserves full credit for the important discovery presented in this paper; I simply tagged along as his ''physics'' doctoral dissertation advisor and harshest skeptic.

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==A Primary Result==
They show, for example, that when expressed in terms of cylindrical coordinates, the axisymmetric potential is,
<div align="center">
<math>
\Phi(R,z) = - \frac{2G}{R^{1/2}} q_0 ,
</math>
</div>
where,
<div align="center">
<math>
q_0 = \int\int (R')^{1/2} \rho(R',z') Q_{-1/2}(\Chi) dR' dz',
</math>
</div>
and the dimensionless argument (the modulus) of the special function, <math>~Q_{-1/2}</math>, is,
<div align="center">
<math>
\Chi \equiv \frac{R^2 + {R'}^2 + (z - z')^2}{2R R'} .
</math>
</div>
Note:  Here we are using <math>~\Chi</math> instead of <math>~\chi</math> (as used by CT99) to represent this dimensionless parameter in order to avoid confusion with our use of <math>~\chi</math>, above.  Next, following the lead of CT99, we note that according to the Abramowitz &amp; Stegun (1965),
<div align="center">
<math>Q_{-1/2}(\Chi) = \mu K(\mu) \, ,</math>
</div>
where, the function <math>~K(\mu)</math> is the complete elliptical integral of the first kind and, for our particular problem,
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>~\mu^2</math>
  </td>
  <td align="center">
<math>~\equiv</math>
  </td>
  <td align="left">
<math>~2(1+\Chi)^{-1}</math>
  </td>
</tr>

<tr>
  <td align="right">
&nbsp;
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>~
2\biggl[ 1+\frac{R^2 + {R'}^2 + (z - z')^2}{2R R'} \biggr]^{-1}
</math>
  </td>
</tr>

<tr>
  <td align="right">
&nbsp;
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>~
\biggl[\frac{4R R'}{(R + {R'})^2 + (z - z')^2} \biggr] \, .
</math>
  </td>
</tr>
</table>
</div>

Hence, we can write,
<div align="center">
<math>
q_0 = \int\int (R')^{1/2} \rho(R',z') \mu K(\mu) dR' dz' \, .
</math>
</div>
-->