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http://functions.wolfram.com/11.13.03.0004.01
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SpheroidalQSPrime[\[Nu], 1/2, 0, z] == (1/(2 (1 - z^2)^(5/4))) Sqrt[Pi/2]
(Sqrt[1 - z^2] (1 + 2 \[Nu]) Cos[(1/2 + \[Nu]) ArcCos[z]] -
z Sin[(1/2 + \[Nu]) ArcCos[z]])
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Cell[BoxData[RowBox[List[RowBox[List["SpheroidalQSPrime", "[", RowBox[List["\[Nu]", ",", FractionBox["1", "2"], ",", "0", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["5", "/", "4"]]], " "]]], SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ")"]], " ", RowBox[List["ArcCos", "[", "z", "]"]]]], "]"]]]], "-", RowBox[List["z", " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ")"]], " ", RowBox[List["ArcCos", "[", "z", "]"]]]], "]"]]]]]], ")"]]]]]]]]
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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> QS </mi> <mrow> <mi> ν </mi> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </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["QS", "IT"], RowBox[List[TagBox["\[Nu]", SpheroidalQSPrime, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], SpheroidalQSPrime, Rule[Editable, True], Rule[Selectable, True]]]]], "\[Prime]"], "(", RowBox[List[TagBox["0", SpheroidalQSPrime, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["z", SpheroidalQSPrime, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[SpheroidalQSPrime[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mrow> <msqrt> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </msqrt> <mtext> </mtext> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SpheroidalQSPrime </ci> <ci> ν </ci> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 5 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arccos /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arccos /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SpheroidalQSPrime", "[", RowBox[List["\[Nu]_", ",", FractionBox["1", "2"], ",", "0", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ")"]], " ", RowBox[List["ArcCos", "[", "z", "]"]]]], "]"]]]], "-", RowBox[List["z", " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ")"]], " ", RowBox[List["ArcCos", "[", "z", "]"]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["5", "/", "4"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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