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StruveL




Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Identities > Recurrence identities > Distant neighbors > Decreasing





http://functions.wolfram.com/03.10.17.0008.01









  


  








Input Form





StruveL[\[Nu], z] == (2^(1 - \[Nu]) z^(-3 + \[Nu]) (2 - z^2 - 6 \[Nu] + 4 \[Nu]^2))/ (Sqrt[Pi] Gamma[1/2 + \[Nu]]) - (2 (-1 + \[Nu]) StruveL[-3 + \[Nu], z])/ z + (1 + (4 (-2 + \[Nu]) (-1 + \[Nu]))/z^2) StruveL[-2 + \[Nu], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["StruveL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["2", "-", SuperscriptBox["z", "2"], "-", RowBox[List["6", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List[SqrtBox["\[Pi]"], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], "z"], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]]]], SuperscriptBox["z", "2"]]]], ")"]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ",", "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> <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> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <msup> <mn> 2 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 3 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mi> z </mi> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> StruveL </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -3 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> StruveL </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> StruveL </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -3 </cn> </apply> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveL", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["2", "-", SuperscriptBox["z", "2"], "-", RowBox[List["6", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], "z"], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]]]], SuperscriptBox["z", "2"]]]], ")"]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]]]]]]]]


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





2002-12-18