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StruveL




Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Specific values > Specialized values > For fixed z > Explicit rational nu





http://functions.wolfram.com/03.10.03.0017.01









  


  








Input Form





StruveL[11/2, z] == (1/(1920 Sqrt[2 Pi] z^(11/2))) (3628800 - 201600 z^2 + 7200 z^4 - 240 z^6 + 10 z^8 - z^10 - 57600 (63 + 28 z^2 + z^4) Cosh[z] + 3840 z (945 + 105 z^2 + z^4) Sinh[z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["StruveL", "[", RowBox[List[FractionBox["11", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1920", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]], RowBox[List["(", RowBox[List["3628800", "-", RowBox[List["201600", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7200", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["240", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["10", " ", SuperscriptBox["z", "8"]]], "-", SuperscriptBox["z", "10"], "-", RowBox[List["57600", " ", RowBox[List["(", RowBox[List["63", "+", RowBox[List["28", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "4"]]], ")"]], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["3840", " ", "z", " ", RowBox[List["(", RowBox[List["945", "+", RowBox[List["105", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "4"]]], ")"]], " ", RowBox[List["Sinh", "[", "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> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1920 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 240 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 201600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3840 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 105 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 945 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 57600 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 28 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 63 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3628800 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> StruveL </ci> <cn type='rational'> 11 <sep /> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1920 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 201600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3840 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 945 </cn> </apply> <apply> <sinh /> <ci> z </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 57600 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 63 </cn> </apply> <apply> <cosh /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 3628800 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveL", "[", RowBox[List[FractionBox["11", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["3628800", "-", RowBox[List["201600", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7200", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["240", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["10", " ", SuperscriptBox["z", "8"]]], "-", SuperscriptBox["z", "10"], "-", RowBox[List["57600", " ", RowBox[List["(", RowBox[List["63", "+", RowBox[List["28", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "4"]]], ")"]], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["3840", " ", "z", " ", RowBox[List["(", RowBox[List["945", "+", RowBox[List["105", " ", SuperscriptBox["z", "2"]]], "+", SuperscriptBox["z", "4"]]], ")"]], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], RowBox[List["1920", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]]]]]]


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





2002-12-18