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http://functions.wolfram.com/11.12.03.0001.01
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SpheroidalPSPrime[\[Nu], \[Mu], 0, z] ==
((-z) (1 + \[Nu]) LegendreP[\[Nu], \[Mu], 2, z] +
(1 - \[Mu] + \[Nu]) LegendreP[1 + \[Nu], \[Mu], 2, z])/(-1 + z^2)
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Cell[BoxData[RowBox[List[RowBox[List["SpheroidalPSPrime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "0", ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["LegendreP", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], ")"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", "2", ",", "z"]], "]"]]]]]], RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <msup> <msub> <mi> PS </mi> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SuperscriptBox[SubscriptBox[StyleBox["PS", "IT"], RowBox[List[TagBox["\[Nu]", SpheroidalPSPrime, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["\[Mu]", SpheroidalPSPrime, Rule[Editable, True], Rule[Selectable, True]]]]], "\[Prime]"], "(", RowBox[List[TagBox["0", SpheroidalPSPrime, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["z", SpheroidalPSPrime, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[SpheroidalPSPrime[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo>  </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox["P", LegendreP] </annotation> </semantics> <mi> ν </mi> <mi> μ </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox["z", HoldComplete[LegendreP, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox["P", LegendreP] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mi> μ </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox["z", HoldComplete[LegendreP, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SpheroidalPSPrime </ci> <ci> ν </ci> <ci> μ </ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> LegendreP </ci> <ci> ν </ci> <ci> μ </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> μ </ci> </apply> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> LegendreP </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <ci> μ </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SpheroidalPSPrime", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "0", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["LegendreP", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], ")"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", "2", ",", "z"]], "]"]]]]]], RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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