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StruveH




Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Integral representations > Contour integral representations





http://functions.wolfram.com/03.09.07.0005.01









  


  








Input Form





StruveH[\[Nu], z] == (z^(1 + \[Nu]) (1/(2 Pi I)) ContourIntegral[(Gamma[s + (\[Nu] + 1)/2] Gamma[(1 - \[Nu])/2 - s])/ (Gamma[1 + \[Nu]/2 - s] Gamma[1 - \[Nu]/2 - s])/(z^2/4)^s, \[ScriptCapitalL]["s"]])/(z^2)^((1 + \[Nu])/2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["StruveH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["z", RowBox[List["1", "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["-", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"]]]], FractionBox["1", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"]]], "]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "-", "s"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "+", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]], RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "2"], "4"], ")"]], RowBox[List["-", "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]]]]]]








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> H </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveH </ci> </annotation-xml> </semantics> </mstyle> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mi> z </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mo> &#8747; </mo> <mi> &#8466; </mi> </msub> <mrow> <mfrac> <mrow> <mrow> <mi> &#915; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveH", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]]]]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "-", "s"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "2"], "4"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "+", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]]]]


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





2001-10-29