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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/11.15.13.0001.01









  


  










Input Form





(1 - z^2) Derivative[2][w][z] - 2 z (2 + (\[Mu]^2 + (1 - z^2)^2 \[Gamma]^2)/ (\[Mu]^2 - (1 - z^2) (SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]] + (1 - z^2) \[Gamma]^2))) Derivative[1][w][z] + (-(\[Mu]^2/(1 - z^2)) + (1 - z^2) \[Gamma]^2 - 2 + SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]] + (4 z^2 (\[Mu]^2 + (1 - z^2)^2 \[Gamma]^2))/ ((1 - z^2) (\[Mu]^2 - (1 - z^2)^2 \[Gamma]^2 - (1 - z^2) SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]))) w[z] == 0 /; w[z] == Subscript[c, 1] SpheroidalS2Prime[\[Nu], \[Mu], \[Gamma], z] + Subscript[c, 2] SpheroidalS1Prime[\[Nu], \[Mu], \[Gamma], z]










Standard Form





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MathML Form







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</ci> <ci> &#956; </ci> <ci> &#947; </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> SpheroidalS1Prime </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "-", RowBox[List["2", " ", "z_", " ", RowBox[List["(", RowBox[List["2", "+", FractionBox[RowBox[List[SuperscriptBox["\[Mu]_", "2"], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], "2"], " ", SuperscriptBox["\[Gamma]_", "2"]]]]], RowBox[List[SuperscriptBox["\[Mu]_", "2"], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["SpheroidalEigenvalue", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_"]], "]"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]_", "2"]]]]], ")"]]]]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Mu]_", "2"], RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]_", "2"]]], "-", "2", "+", RowBox[List["SpheroidalEigenvalue", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_"]], "]"]], "+", FractionBox[RowBox[List["4", " ", SuperscriptBox["z_", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Mu]_", "2"], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], "2"], " ", SuperscriptBox["\[Gamma]_", "2"]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Mu]_", "2"], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], "2"], " ", SuperscriptBox["\[Gamma]_", "2"]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], ")"]], " ", RowBox[List["SpheroidalEigenvalue", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_"]], "]"]]]]]], ")"]]]]]]], ")"]], " ", RowBox[List["w", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], " ", RowBox[List["SpheroidalS2Prime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", RowBox[List["SpheroidalS1Prime", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", "z"]], "]"]]]]]]]]]]]]]]










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





2007-05-02





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