Editing Appendix/Ramblings (section)

=Mathematics=
<ol>
  <li>Roots of Cubic Equation</li>
      <ol style="list-style-type:lower-latin">
          <li>In the context of [[Appendix/Ramblings/T1Coordinates#Second_Special_Case_.28cubic.29|T2 Coordinates]], when <math>q^2 = (a_1/a_3)^2=3</math>.</li>
          <li>[[Appendix/Ramblings/PPToriPt1A#Cubic_Equation_Solution|PP Tori]] &#8212; Also includes [[Appendix/Ramblings/PPToriPt1A#CubeRootImaginary|cube root of a complex number]]</li>
          <li>[[SSC/Structure/Polytropes#CubicRoot|Srivastava's F-Type solution]] for <math>n=5</math> polytropes.</li>
          <li>[[SSC/Structure/BiPolytropes/Analytic15#Analytic_Solution_of_Key_Interface_Relation|Murphy &amp; Fiedler's Bipolytrope]] with <math>(n_c, n_e) = (1,5)</math></li>
          <li>[[Appendix/Ramblings/AdditionalAnalyticallySpecifiedEigenvectors00Bipolytropes#Solve_Cubic_Equation|Analytic Eigenfunctions for Bipolytropes]] with <math>(n_c, n_e) = (0, 0)</math> &#8212; also involves cube root of a complex number</li>
       </ol>
  <li> Roots of Quartic Equation</li>
      <ol style="list-style-type:lower-latin">
         <li>[[SSC/Stability/BiPolytrope00Details#Roots_of_Quartic_Equation|Analytic Eigenfunction for Bipolytropes]] with <math>(n_c, n_e) = (0, 0)</math></li>
         <li>[[SR/Ptot_QuarticSolution#Quartic_Equation_Solution|Determine temperature from total pressure]]
      </ol>
  <li>Singular Sturm-Liouville (eigenvalue) Problem</li>
      <ol style="list-style-type:lower-latin">
          <li>[[Apps/Blaes85SlimLimit#Singular_Sturm-Liouville_Problem|Oscillations of PP Tori]] in the slim torus limit</li>
          <li>[[Apps/ImamuraHadleyCollaboration#Singular_Sturm-Liouville_Problem|Characteristics of unstable eigenvectors in self-gravitating tori]]</li>
     </ol>
  <li>[[Appendix/Ramblings/PowerSeriesExpressions|Approximate Power-Series Expressions]]</li>
  <li>[[Appendix/Ramblings/FourierSeries|Fourier Series]]</li>
  <li>[[Appendix/Ramblings/TrigFunctions|Analytic Expressions for Selected Trigonometric Functions]]</li>
  <li>[[AxisymmetricConfigurations/PoissonEq#Special_Functions_.26_Other_Broadly_Used_Representations|Special Functions &amp; Other Broadly Used Representations]]</li>
      <ol>
        <li>[[AxisymmetricConfigurations/PoissonEq#Spherical_Harmonics_and_Associated_Legendre_Functions|Spherical Harmonics and Associated Legendre Functions]]</li>
        <li>[[AxisymmetricConfigurations/PoissonEq#Multipole_Expansions|Multipole Expansions]]</li>
        <li>[[AxisymmetricConfigurations/PoissonEq#Familiar_Expression_for_the_Cylindrical_Green.27s_Function_Expansion|Familiar Expression for the Cylindrical Green's Function Expansion]]</li>
        <li>[[AxisymmetricConfigurations/PoissonEq#Toroidal_Functions|Toroidal Functions]]</li>
      </ol>
  <li>Green's Function in terms of Toroidal Functions</li>
      <ol style="list-style-type:lower-latin">
          <li>[[Appendix/Ramblings/CCGF|Compact Cylindrical Green Function]]</li>
          <li>[[Appendix/Ramblings/ToroidalCoordinates#Relating_CCGF_Expansion_to_Toroidal_Coordinates|Toroidal configurations &amp; related coordinate systems]] &#8212; Includes <b><font color="red">EUREKA!</font></b> moment; also uses [[Appendix/Ramblings/ToroidalCoordinates#Examples|wikitable overflow]] (scrolling) box</li>
          <li>[[2DStructure/ToroidalCoordinateIntegrationLimits#Evaluation_of_Elliptic_Integrals|Toroidal Coordinate Integration Limits]] <math>\Leftarrow ~~</math>  Includes Table of Example K(k) and E(k) Function Values; see a separate set of K(k) and E(k) evaluations in the context of [[Apps/DysonPotential#Our_Attempt_to_Replicate|Our Attempt to Replicate]] Dyson's results.</li>
          <li>[[2DStructure/ToroidalCoordinates#Using_Toroidal_Coordinates_to_Determine_the_Gravitational_Potential|Using Toroidal Coordinates to Determine the Gravitational Potential]] (Initial Presentation)</li>
          <li>[[2DStructure/ToroidalGreenFunction#Appendix_B:_Elliptic_Integrals|Using Toroidal Coordinates to Determine the Gravitational Potential]] (Improved Presentation) &nbsp; <math>\Leftarrow</math>&nbsp; &nbsp; includes [[2DStructure/ToroidalGreenFunction#Series_Expansions|series expansions]] for K(k) and E(k)</li>
          <li>[[Appendix/Mathematics/ToroidalFunctions|Relationships between Toroidal Functions]] <math>\Leftarrow ~~</math> 5 plots of [<b>[[Appendix/References#MF53|<font color="red">MF53</font>]]</b>] data included here</li>
          <li>[[Appendix/Mathematics/ToroidalConfusion|Confusion Regarding Whipple Formulae]]</li>
          <li>[[Appendix/Mathematics/ToroidalSynopsis01|Pulling It All Together]] <math>\Leftarrow ~~</math> 2 additional plots of [<b>[[Appendix/References#MF53|<font color="red">MF53</font>]]</b>] data included here</li>
      </ol>
<li>[[Appendix/Mathematics/ScaleFactors|Scale Factors for Orthogonal Curvilinear Coordinate Systems]]</li>
<li>[[Appendix/Mathematics/EulerAngles|Euler Angles]]</li>
<li>[[Appendix/Mathematics/StepFunction|Step Function and its Derivative]]</li>
<li>[[Appendix/Mathematics/Hypergeometric|Hypergeometric Equation and Its Solutions]]</li>
</ol>