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Cell[CellGroupData[{
Cell["Physics 70006  E&M I", "Subtitle"],

Cell["Generalized Legendre Functions", "Subsubtitle"],

Cell[CellGroupData[{

Cell["Conical Harmonics", "Subsection"],

Cell[BoxData[
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Cell["\<\
P[\[Nu], \[Theta]] is a generalized Legendre function. We want to force it to \
be a conical harmonic associated with opening half-angle \[Beta]. \
\>", "Text",
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Cell[BoxData[
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Cell["\<\
From the graph, one sees that the approximate roots for this value of \[Beta] \
are at \[Nu]app = 2.5, 6.5, 10.5, 14.5, ..v  (spacing is 4) . Now, let's \
obtain more precise values starting from \[Vee]app.\
\>", "Text",
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for \[Theta]<\[Beta].",
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        P[\[Nu]1[\([4]\)], \[Theta]], P[\[Nu]1[\([5]\)], \[Theta]], 
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Cell[TextData[StyleBox["Near the vertex of the cone \[Nu]0 = \[Nu]1[1]  will \
dominate the series expansion for the potential",
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Cell[BoxData[
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Cell[BoxData[
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      r^\[Nu]0\ P[\[Nu]0, \[Theta]]\)], "Input"],

Cell[BoxData[
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            r, \[Theta]], \[Theta]]\)], "Input"],

Cell[BoxData[
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      PlotStyle \[Rule] {Hue[0.6], Thickness[0.008]}, 
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Cell["Potential plot", "Subsection"],

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      Piecewise[{{\[CapitalPhi][
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\[Beta]}}]\)], "Input"],

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        ContourSmoothing \[Rule] \ 
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