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Combined display of all available logs of JETohlineWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 13:38, 30 June 2024 Joel2 talk contribs created page File:Apollonian myway7B.png
- 13:38, 30 June 2024 Joel2 talk contribs uploaded File:Apollonian myway7B.png
- 13:37, 30 June 2024 Joel2 talk contribs created page File:ConstantXi2.png
- 13:37, 30 June 2024 Joel2 talk contribs uploaded File:ConstantXi2.png
- 13:36, 30 June 2024 Joel2 talk contribs created page File:Apollonian myway5B.png
- 13:36, 30 June 2024 Joel2 talk contribs uploaded File:Apollonian myway5B.png
- 13:34, 30 June 2024 Joel2 talk contribs created page File:MergedTorus01.png
- 13:34, 30 June 2024 Joel2 talk contribs uploaded File:MergedTorus01.png
- 13:34, 30 June 2024 Joel2 talk contribs created page File:SimpleTorusIllustration.png
- 13:34, 30 June 2024 Joel2 talk contribs uploaded File:SimpleTorusIllustration.png
- 13:32, 30 June 2024 Joel2 talk contribs created page 2DStructure/ToroidalCoordinateIntegrationLimits (Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Toroidal-Coordinate Integration Limits= In support of our accompanying discussion of the gravitational potential of a uniform-density circular torus, here we explain in detail what limits of integration must be specified in order to accurately determine the ''v...")
- 18:51, 29 June 2024 Joel2 talk contribs created page Template:Math/EQ Toroidal08 (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions </td> <td align="right"> <math> Q_{-\frac{1}{2}}^\mu(z) + 2\sum_{n=1}^\infty Q^\mu_{n-\frac{1}{2}}(z) \cos(n\nu) </math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> e^{i\mu\pi}~\biggl(\frac{\pi}{2} \biggr)^{1 / 2} \Gamma(\mu + \tfrac{1}{2})\b...")
- 18:50, 29 June 2024 Joel2 talk contribs created page Template:Math/EQ Toroidal06 (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions </td> <td align="right"> <math>(\xi - z)\sum_{m=0}^n (2m+1)P_m(z) Q_m(\xi)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> 1 - (\ell+1)[P_{\ell+1}(z) Q_\ell(\xi) - P_\ell(z)Q_{\ell+1}(\xi)] </math> </td> </tr> <tr> <td align="center"...")
- 18:49, 29 June 2024 Joel2 talk contribs created page Template:Math/EQ Toroidal05 (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions </td> <td align="right"> <math> \int_a^b\biggl[(\nu - \sigma)(\nu + \sigma + 1) + (\rho^2 - \mu^2)(1 - z^2)^{-1} \biggr] w_\nu^\mu ~w_\sigma^\rho ~dz </math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> \biggl[ z(\nu-\sigma) w_\nu^\mu ~w_\sigm...")
- 18:47, 29 June 2024 Joel2 talk contribs created page Template:Math/EQ Toroidal03 (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions </td> <td align="right"> <math>Q_\nu^\mu(z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> e^{i \mu \pi} ~ (2\pi)^{-\frac{1}{2}} (z^2-1)^{\mu/2} ~\Gamma(\mu + \tfrac{1}{2})~\biggl\{ \int_0^\pi (z - \cos t)^{-\mu - \frac{1}{2}} \cos[(\nu +...")
- 18:13, 29 June 2024 Joel2 talk contribs created page File:RoverDunity.png
- 18:13, 29 June 2024 Joel2 talk contribs uploaded File:RoverDunity.png
- 18:12, 29 June 2024 Joel2 talk contribs created page File:RoverD5over1.png
- 18:12, 29 June 2024 Joel2 talk contribs uploaded File:RoverD5over1.png
- 18:11, 29 June 2024 Joel2 talk contribs created page File:RoverDinfty.png
- 18:11, 29 June 2024 Joel2 talk contribs uploaded File:RoverDinfty.png
- 18:07, 29 June 2024 Joel2 talk contribs created page File:Q0minus1Half.png
- 18:07, 29 June 2024 Joel2 talk contribs uploaded File:Q0minus1Half.png
- 18:00, 29 June 2024 Joel2 talk contribs created page Appendix/Mathematics/ToroidalConfusion (Created page with "<!-- __NOTOC__ will force TOC off --> __FORCETOC__ =Confusion Regarding Whipple Formulae= May, 2018 (J.E.Tohline): I am trying to figure out what the correct relationship is between half-integer degree, associated Legendre functions of the first and second kinds. In order to illustrate my current confusion, here I will restrict my presentation to expressions that give <math>~Q^m_{n - 1 / 2}(\cosh\eta)</math> in terms of <math>~P^n_{m - 1 / 2}(\coth\eta)</math>. ==Pu...")
- 17:58, 29 June 2024 Joel2 talk contribs created page File:ToroidalRecurrenceRelation.png
- 17:58, 29 June 2024 Joel2 talk contribs uploaded File:ToroidalRecurrenceRelation.png
- 17:57, 29 June 2024 Joel2 talk contribs created page File:AbramowitzStegun ToroidalFunctions2.png
- 17:57, 29 June 2024 Joel2 talk contribs uploaded File:AbramowitzStegun ToroidalFunctions2.png
- 17:55, 29 June 2024 Joel2 talk contribs created page Template:Math/EQ Toroidal02 (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions </td> <td align="right"> <math>Q_{n-1 / 2}^m (\lambda)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math>(-1)^n \frac{\pi^{3/2}}{\sqrt{2}~ \Gamma(n-m+1 / 2)} (x^2-1)^{1 / 4} P_{m-1 / 2}^n(x) \, , </math> </td> </tr> <tr> <td align="center...")
- 17:52, 29 June 2024 Joel2 talk contribs created page File:Q0plus3Half.png
- 17:52, 29 June 2024 Joel2 talk contribs uploaded File:Q0plus3Half.png
- 17:52, 29 June 2024 Joel2 talk contribs created page File:Q0plus1Half.png
- 17:52, 29 June 2024 Joel2 talk contribs uploaded File:Q0plus1Half.png
- 17:50, 29 June 2024 Joel2 talk contribs created page File:P0plusHalf.png
- 17:50, 29 June 2024 Joel2 talk contribs uploaded File:P0plusHalf.png
- 17:50, 29 June 2024 Joel2 talk contribs created page File:P0minusHalf.png
- 17:50, 29 June 2024 Joel2 talk contribs uploaded File:P0minusHalf.png
- 17:39, 29 June 2024 Joel2 talk contribs created page Appendix/Mathematics/ToroidalFunctions (Created page with "<!-- __NOTOC__ will force TOC off --> __FORCETOC__ =Relationships Between Toroidal Functions= ==Wong Toroidal Coordinates== ===Wong's Expression for the Potential=== This chapter has been put together in an effort to lay the groundwork for an evaluation of Wong's (1973) derived expression for the gravitational potential both inside and outside of a uniform-density, axisymmetric torus. After multiplying his expression by...")
- 17:34, 29 June 2024 Joel2 talk contribs created page File:Q2minus1Half3.png
- 17:34, 29 June 2024 Joel2 talk contribs uploaded File:Q2minus1Half3.png
- 17:34, 29 June 2024 Joel2 talk contribs created page File:ABSQ1minus1Half3.png
- 17:34, 29 June 2024 Joel2 talk contribs uploaded File:ABSQ1minus1Half3.png
- 17:32, 29 June 2024 Joel2 talk contribs created page File:Q0plus1Half3.png
- 17:32, 29 June 2024 Joel2 talk contribs uploaded File:Q0plus1Half3.png
- 17:31, 29 June 2024 Joel2 talk contribs created page File:P0plus1Half4.png
- 17:31, 29 June 2024 Joel2 talk contribs uploaded File:P0plus1Half4.png
- 17:30, 29 June 2024 Joel2 talk contribs created page File:Q0minus1Half3.png
- 17:30, 29 June 2024 Joel2 talk contribs uploaded File:Q0minus1Half3.png
- 17:28, 29 June 2024 Joel2 talk contribs created page File:P0minus1Half3.png
- 17:28, 29 June 2024 Joel2 talk contribs uploaded File:P0minus1Half3.png
