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http://functions.wolfram.com/05.02.13.0003.01
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Derivative[2][w][z] + (-Derivative[1][g][z] + Derivative[1][g][z]/g[z] -
Derivative[2][g][z]/Derivative[1][g][z]) Derivative[1][w][z] +
((n Derivative[1][g][z]^2)/g[z]) w[z] == 0 /;
w[z] == Subscript[c, 1] LaguerreL[n, g[z]] +
Subscript[c, 2] MeijerG[{{}, {n + 1}}, {{0, 0}, {}}, -g[z]]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "+", RowBox[List[RowBox[List["(", " ", RowBox[List[RowBox[List["-", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List["g", "[", "z", "]"]]], "-", FractionBox[RowBox[List[" ", RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]]], ")"]], RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[FractionBox[RowBox[List["n", " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"]]], RowBox[List["g", "[", "z", "]"]]], RowBox[List["w", "[", "z", "]"]]]]]], "\[Equal]", "0"]], "/;", " ", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["n", "+", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["-", RowBox[List["g", "[", "z", "]"]]]]]], "]"]]]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msup> <mi> w </mi> <mi> ′′ </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mi> g </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> - </mo> <mrow> <msup> <mi> g </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> g </mi> <mi> ′′ </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <msup> <mi> g </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> g </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo>  </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <msub> <mi> L </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> c </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "2"]], RowBox[List["2", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", RowBox[List["g", "(", "z", ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[RowBox[List["n", "+", "1"]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> LaguerreL </ci> <ci> n </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </list> <list /> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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