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http://functions.wolfram.com/11.08.03.0006.01
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SpheroidalPS[\[Nu], 1/2, 0, z] == (Sqrt[Pi]/(Sqrt[2] (1 - z^2)^(1/4)))
ChebyshevT[\[Nu] + 1/2, z]
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Cell[BoxData[RowBox[List[RowBox[List["SpheroidalPS", "[", RowBox[List["\[Nu]", ",", FractionBox["1", "2"], ",", "0", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SqrtBox["\[Pi]"], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["1", "/", "4"]]], " "]]], RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "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> <msub> <mi> PS </mi> <mrow> <mi> ν </mi> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[StyleBox["PS", "IT"], RowBox[List[TagBox["\[Nu]", SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]]]]], "(", RowBox[List[TagBox["0", SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["z", SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[SpheroidalPS[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <msqrt> <mi> π </mi> </msqrt> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 4 </mn> </mroot> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mi> T </mi> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SpheroidalPS </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 /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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 /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> ChebyshevT </ci> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SpheroidalPS", "[", RowBox[List["\[Nu]_", ",", FractionBox["1", "2"], ",", "0", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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