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SpheroidalS2Prime






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > SpheroidalS2Prime[nu,mu,gamma,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/11.15.13.0008.01









  


  










Input Form





Wronskian[z^s SpheroidalS2Prime[\[Nu], \[Mu], \[Gamma], a z^r], z^s SpheroidalS1Prime[\[Nu], \[Mu], \[Gamma], a z^r], z] == a r z^(2 s + r - 1) (\[Gamma]^2/(1 - a^2 z^(2 r)) - \[Mu]^2/(1 - a^2 z^(2 r))^3 + SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]/ (1 - a^2 z^(2 r))^2) (SpheroidalS1Prime[\[Nu], \[Mu], \[Gamma], 0] SpheroidalS2[\[Nu], \[Mu], \[Gamma], 0] - SpheroidalS1[\[Nu], \[Mu], \[Gamma], 0] SpheroidalS2Prime[\[Nu], \[Mu], \[Gamma], 0])










Standard Form





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MathML Form







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</ci> <ci> &#956; </ci> <ci> &#947; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> s </ci> </apply> <apply> <ci> SpheroidalS1Prime </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> r </ci> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> r </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> &#947; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> &#956; 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</ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <ci> SpheroidalS2 </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> SpheroidalS1 </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <ci> SpheroidalS2Prime </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["z_", "s_"], " ", RowBox[List["SpheroidalS2Prime", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_", ",", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z_", "s_"], " ", RowBox[List["SpheroidalS1Prime", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_", ",", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["a", " ", "r", " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "s"]], "+", "r", "-", "1"]]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["\[Gamma]", "2"], RowBox[List["1", "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "r"]]]]]]]], "-", FractionBox[SuperscriptBox["\[Mu]", "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "r"]]]]]]], ")"]], "3"]], "+", FractionBox[RowBox[List["SpheroidalEigenvalue", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]"]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "r"]]]]]]], ")"]], "2"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["SpheroidalS1Prime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "0"]], "]"]], " ", RowBox[List["SpheroidalS2", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "0"]], "]"]]]], "-", RowBox[List[RowBox[List["SpheroidalS1", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "0"]], "]"]], " ", RowBox[List["SpheroidalS2Prime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "0"]], "]"]]]]]], ")"]]]]]]]]










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





2007-05-02