Angular spheroidal function of the second kind: General characteristics (formula 11.09.04.0001)

SpheroidalQS

$Mathematica Notation$

Mathieu and Spheroidal Functions

SpheroidalQS[nu,mu,gamma,z]

General characteristics

Domain and analyticity

http://functions.wolfram.com/11.09.04.0001.01

Input Form

DomainAndRange[Function[{\[Nu], \[Mu], \[Gamma], z}, SpheroidalQS[\[Nu], \[Mu], \[Gamma], z]]] == ProductSet[Complexes, Complexes, Complexes, Complexes] \[LongRightArrow] Complexes

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "}"]], ",", RowBox[List["SpheroidalQS", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "]"]]]], "]"]], "]"]], "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes", ",", "Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> ⋆ </mo> <mi> μ </mi> <mo> ⋆ </mo> <mrow> <mi> γ </mi> <mo> * </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <semantics> <mrow> <msub> <mi> QS </mi> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> γ </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[StyleBox["QS", "IT"], RowBox[List[TagBox["\[Nu]", SpheroidalQS, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["\[Mu]", SpheroidalQS, Rule[Editable, True], Rule[Selectable, True]]]]], "(", RowBox[List[TagBox["\[Gamma]", SpheroidalQS, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["z", SpheroidalQS, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[SpheroidalQS[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> <mo> ∷ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> ℂ </mi> <mo> ⊗ </mo> <mi> ℂ </mi> <mo> ⊗ </mo> <mi> ℂ </mi> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <mi> ℂ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <ci> ν </ci> <ci> μ </ci> <apply> <times /> <ci> γ </ci> <ci> z </ci> </apply> </apply> <apply> <ci> SpheroidalQS </ci> <ci> ν </ci> <ci> μ </ci> <ci> γ </ci> <ci> z </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <ci> ℂ </ci> <ci> ℂ </ci> <ci> ℂ </ci> <ci> ℂ </ci> </apply> <ci> ℂ </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_", ",", "z_"]], "}"]], ",", RowBox[List["SpheroidalQS", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_", ",", "z_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes", ",", "Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]

Date Added to functions.wolfram.com (modification date)

2007-05-02