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http://functions.wolfram.com/03.09.27.0004.01
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StruveH[\[Nu], z] == (-1)^(\[Nu] + 1/2) BesselJ[-\[Nu], z] /;
Element[-\[Nu] - 1/2, Integers] && -\[Nu] - 1/2 >= 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StruveH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]]], RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", "z"]], "]"]]]]]], "/;", " ", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", FractionBox["1", "2"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", FractionBox["1", "2"]]], "\[GreaterEqual]", "0"]]]]]]]]
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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> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveH </ci> </annotation-xml> </semantics> </mstyle> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> J </mi> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> StruveH </ci> <ci> ν </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> BesselJ </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <in /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> ℕ </ci> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveH", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]]], " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", "z"]], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", FractionBox["1", "2"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", FractionBox["1", "2"]]], "\[GreaterEqual]", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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