html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 StruveH

 http://functions.wolfram.com/03.09.21.0016.01

 Input Form

 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]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", 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"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], ")"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["z", RowBox[List["2", "+", "\[Mu]", "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]"]], "]"]]]]], RowBox[List["(", 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["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"]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z μ + ν + 1 J ν ( z ) H StruveH μ ( z ) z z μ + ν + 2 4 ( μ + ν + 1 ) ( - 2 - μ - ν z μ + ν + 1 Γ ( μ + ν + 3 2 ) π Γ ( μ + 3 2 ) 1 F ~ 2 ( μ + ν + 3 2 ; ν + 1 , μ + ν + 5 2 ; - z 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["\[Mu]", "+", "\[Nu]", "+", FractionBox["3", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["\[Nu]", "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["\[Mu]", "+", "\[Nu]", "+", FractionBox["5", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] + 2 J ν ( z ) H StruveH μ ( z ) + 2 J ν + 1 ( z ) H StruveH μ + 1 ( z ) ) z z μ ν 1 BesselJ ν z StruveH μ z z μ ν 2 4 μ ν 1 -1 -1 2 -1 μ -1 ν z μ ν 1 Gamma μ ν 3 2 1 2 Gamma μ 3 2 -1 HypergeometricPFQRegularized μ ν 3 2 ν 1 μ ν 5 2 -1 z 2 4 -1 2 BesselJ ν z StruveH μ z 2 BesselJ ν 1 z StruveH μ 1 z [/itex]

 Rule Form

 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]"]], ")"]]]]]]]]]

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

 2001-10-29