Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











StruveL






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/03.10.13.0007.01









  


  










Input Form





Derivative[3][w][z] - ((((-2 + \[Nu]) Derivative[1][g][z])/g[z]) ((3 Derivative[2][g][z])/Derivative[1][g][z])) Derivative[2][w][z] + (-Derivative[1][g][z]^2 - (\[Nu] (1 + \[Nu]) Derivative[1][g][z]^2)/ g[z]^2 + ((-2 + \[Nu]) Derivative[2][g][z])/g[z] + (3 Derivative[2][g][z]^2)/Derivative[1][g][z]^2 - Derivative[3][g][z]/Derivative[1][g][z]) Derivative[1][w][z] + ((\[Nu]^2 (1 + \[Nu]) Derivative[1][g][z]^3)/g[z]^3 + ((-1 + \[Nu]) Derivative[1][g][z]^3)/g[z]) w[z] == 0 /; w[z] == Subscript[c, 1] StruveL[\[Nu], g[z]] + Subscript[c, 2] BesselI[\[Nu], g[z]] + Subscript[c, 3] BesselK[\[Nu], g[z]]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List["g", "[", "z", "]"]]], FractionBox[RowBox[List["3", " ", RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]]], ")"]], RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"]]], "-", FractionBox[RowBox[List["\[Nu]", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"]]], SuperscriptBox[RowBox[List["g", "[", "z", "]"]], "2"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List["g", "[", "z", "]"]]], "+", FractionBox[RowBox[List["3", " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"]]], SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"]], "-", FractionBox[RowBox[List[SuperscriptBox["g", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]]], ")"]], RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Nu]", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "3"]]], SuperscriptBox[RowBox[List["g", "[", "z", "]"]], "3"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "3"]]], 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["StruveL", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "3"], RowBox[List["BesselK", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]]]]]]]]]]










MathML Form







<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> <semantics> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, &quot;3&quot;, &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> g </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <msup> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> - </mo> <msup> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> g </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <msup> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> g </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> g </mi> <semantics> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, &quot;3&quot;, &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <msup> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> L </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveL </ci> </annotation-xml> </semantics> </mstyle> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <msub> <mi> c </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <msub> <mi> c </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <msub> <mi> K </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </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'> 3 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> g </ci> <ci> z </ci> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#957; </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <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> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <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> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <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> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 3 </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> <plus /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </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> StruveL </ci> <ci> &#957; </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> BesselI </ci> <ci> &#957; </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> BesselK </ci> <ci> &#957; </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]_"]], ")"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["3", " ", RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], ")"]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], RowBox[List[RowBox[List["g", "[", "z_", "]"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "2"]]], "-", FractionBox[RowBox[List["\[Nu]_", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]_"]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "2"]]], SuperscriptBox[RowBox[List["g", "[", "z_", "]"]], "2"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]_"]], ")"]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], RowBox[List["g", "[", "z_", "]"]]], "+", FractionBox[RowBox[List["3", " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "2"]]], SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "2"]], "-", FractionBox[RowBox[List[SuperscriptBox["g", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]], RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Nu]_", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]_"]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "3"]]], SuperscriptBox[RowBox[List["g", "[", "z_", "]"]], "3"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]_"]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "3"]]], RowBox[List["g", "[", "z_", "]"]]]]], ")"]], " ", RowBox[List["w", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], " ", RowBox[List["StruveL", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "3"], " ", RowBox[List["BesselK", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]]]]]]]]]]]]










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





2007-05-02





© 1998-2014 Wolfram Research, Inc.