Derivative of the angular spheroidal function of the first kind: Series representations (formula 11.12.06.0004)

SpheroidalPSPrime

$Mathematica Notation$

Mathieu and Spheroidal Functions

SpheroidalPSPrime[nu,mu,gamma,z]

Series representations

Generalized power series

Expansions at generic point z==z₀

http://functions.wolfram.com/11.12.06.0004.01

Input Form

SpheroidalPSPrime[\[Nu], \[Mu], \[Gamma], z] \[Proportional] SpheroidalPSPrime[\[Nu], \[Mu], \[Gamma], Subscript[z, 0]] (1 + O[z - Subscript[z, 0]])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["SpheroidalPSPrime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["SpheroidalPSPrime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", SubscriptBox["z", "0"]]], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]]]], ")"]]]]]]]]

MathML Form

<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> <mi> γ </mi> <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["\[Gamma]", 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> <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> <mi> γ </mi> <mo> , </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </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["\[Gamma]", SpheroidalPSPrime, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[SubscriptBox["z", "0"], SpheroidalPSPrime, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[SpheroidalPSPrime[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> SpheroidalPSPrime </ci> <ci> ν </ci> <ci> μ </ci> <ci> γ </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <ci> SpheroidalPSPrime </ci> <ci> ν </ci> <ci> μ </ci> <ci> γ </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SpheroidalPSPrime", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["SpheroidalPSPrime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", SubscriptBox["zz", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]]]], ")"]]]]]]]]

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

2007-05-02