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http://functions.wolfram.com/03.09.21.0016.01
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Integrate[z^(1 + \[Mu] + \[Nu]) BesselJ[\[Nu], z] StruveH[\[Mu], z], z] ==
(1/(4 (1 + \[Mu] + \[Nu]))) (z^(2 + \[Mu] + \[Nu])
(-((1/(Sqrt[Pi] Gamma[3/2 + \[Mu]])) (2^(-\[Mu] - \[Nu])
z^(1 + \[Mu] + \[Nu]) Gamma[3/2 + \[Mu] + \[Nu]]
HypergeometricPFQRegularized[{3/2 + \[Mu] + \[Nu]},
{1 + \[Nu], 5/2 + \[Mu] + \[Nu]}, -(z^2/4)])) +
2 BesselJ[\[Nu], z] StruveH[\[Mu], z] + 2 BesselJ[1 + \[Nu], z]
StruveH[1 + \[Mu], z]))
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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> <mo> ∫ </mo> <mrow> <mrow> <msup> <mi> z </mi> <mrow> <mi> μ </mi> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> J </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveH </ci> </annotation-xml> </semantics> </mstyle> <mi> μ </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mrow> <mi> μ </mi> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - 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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["1", "+", "\[Mu]_", "+", "\[Nu]_"]]], " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], " ", RowBox[List["StruveH", "[", RowBox[List["\[Mu]_", ",", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["2", "+", "\[Mu]", "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Mu]"]], "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "+", "\[Nu]"]], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "+", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List[FractionBox["5", "2"], "+", "\[Mu]", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]"]], "]"]]]]]]], "+", RowBox[List["2", " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], " ", RowBox[List["StruveH", "[", RowBox[List["\[Mu]", ",", "z"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["StruveH", "[", RowBox[List[RowBox[List["1", "+", "\[Mu]"]], ",", "z"]], "]"]]]]]], ")"]]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], ")"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
