Derivative of the angular spheroidal function of the first kind: General characteristics (formula 11.12.04.0003)

SpheroidalPSPrime

$Mathematica Notation$

Mathieu and Spheroidal Functions

SpheroidalPSPrime[nu,mu,gamma,z]

General characteristics

Symmetries and periodicities

Parity

http://functions.wolfram.com/11.12.04.0003.01

Input Form

SpheroidalPSPrime[-\[Nu], \[Mu], \[Gamma], z] == SpheroidalPSPrime[\[Nu] - 1, \[Mu], \[Gamma], z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["SpheroidalPSPrime", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "]"]], "\[Equal]", RowBox[List["SpheroidalPSPrime", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "]"]]]]]]

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> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <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[RowBox[List["-", "\[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> <semantics> <mrow> <msup> <msub> <mi> PS </mi> <mrow> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <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[RowBox[List["\[Nu]", "-", "1"]], 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> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SpheroidalPSPrime </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <ci> μ </ci> <ci> γ </ci> <ci> z </ci> </apply> <apply> <ci> SpheroidalPSPrime </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> <ci> μ </ci> <ci> γ </ci> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SpheroidalPSPrime", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", "\[Mu]_", ",", "\[Gamma]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["SpheroidalPSPrime", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "]"]]]]]]

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

2007-05-02