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; }

 StruveL

 http://functions.wolfram.com/03.10.06.0044.01

 Input Form

 StruveL[\[Nu], z] \[Proportional] (Sqrt[2]/(E^(((Pi I)/4) (1 + 2 \[Nu])) (Sqrt[Pi] Sqrt[z]))) (Sinh[((Pi I)/4) (1 + 2 \[Nu]) + z] HypergeometricPFQ[ {(1 - 2 \[Nu])/4, (3 - 2 \[Nu])/4, (1 + 2 \[Nu])/4, (3 + 2 \[Nu])/4}, {1/2}, 1/z^2] + ((1 - 4 \[Nu]^2)/(8 z)) Cosh[((Pi I)/4) (1 + 2 \[Nu]) + z] HypergeometricPFQ[ {(3 - 2 \[Nu])/4, (5 - 2 \[Nu])/4, (3 + 2 \[Nu])/4, (5 + 2 \[Nu])/4}, {3/2}, 1/z^2]) - ((2^(1 - \[Nu]) z^(\[Nu] - 1))/ (Sqrt[Pi] Gamma[1/2 + \[Nu]])) HypergeometricPFQ[{1/2, 1, 1/2 - \[Nu]}, {}, 4/z^2] /; -Pi < Arg[z] < Pi/2 && (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StruveL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]], " "]], RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sinh", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "+", "z"]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["2", "\[Nu]"]]]], "4"], ",", FractionBox[RowBox[List["3", "-", RowBox[List["2", "\[Nu]"]]]], "4"], ",", FractionBox[RowBox[List["1", "+", RowBox[List["2", "\[Nu]"]]]], "4"], ",", FractionBox[RowBox[List["3", "+", RowBox[List["2", "\[Nu]"]]]], "4"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List[" ", RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]]]], RowBox[List["8", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "+", "z"]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", RowBox[List["2", "\[Nu]"]]]], "4"], ",", FractionBox[RowBox[List["5", "-", RowBox[List["2", "\[Nu]"]]]], "4"], ",", FractionBox[RowBox[List["3", "+", RowBox[List["2", "\[Nu]"]]]], "4"], ",", FractionBox[RowBox[List["5", "+", RowBox[List["2", "\[Nu]"]]]], "4"]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]]]], ")"]]]], "-", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["4", SuperscriptBox["z", "2"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

 MathML Form

 L StruveL ν ( z ) 2 - π 4 ( 1 + 2 ν ) π z ( sinh ( z + π 4 ( 2 ν + 1 ) ) 4 F 1 ( 1 - 2 ν 4 , 3 - 2 ν 4 , 2 ν + 1 4 , 2 ν + 3 4 ; 1 2 ; 1 z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "1"]], "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["1", SuperscriptBox["z", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + 1 - 4 ν 2 8 z cosh ( z + π 4 ( 2 ν + 1 ) ) 4 F 1 ( 3 - 2 ν 4 , 5 - 2 ν 4 , 3 + 2 ν 4 , 5 + 2 ν 4 ; 3 2 ; 1 z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], "4"], " "]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["1", SuperscriptBox["z", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) - 2 1 - ν z ν - 1 π Γ ( ν + 1 2 ) 3 F 0 ( 1 2 , 1 , 1 2 - ν ; ; 4 z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["0", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["4", SuperscriptBox["z", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] /; - π < arg ( z ) < π 2 ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional StruveL ν z 2 1 2 -1 4 -1 1 2 ν 1 2 z 1 2 -1 z 4 -1 2 ν 1 HypergeometricPFQ 1 -1 2 ν 4 -1 3 -1 2 ν 4 -1 2 ν 1 4 -1 2 ν 3 4 -1 1 2 1 z 2 -1 1 -1 4 ν 2 8 z -1 z 4 -1 2 ν 1 HypergeometricPFQ 3 -1 2 ν 4 -1 5 -1 2 ν 4 -1 3 2 ν 4 -1 5 2 ν 4 -1 3 2 1 z 2 -1 -1 2 1 -1 ν z ν -1 1 2 Gamma ν 1 2 -1 HypergeometricPFQ 1 2 1 1 2 -1 ν 4 z 2 -1 -1 z 2 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveL", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sinh", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "+", "z"]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "+", "z"]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], RowBox[List["8", " ", "z"]]]]], ")"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["4", SuperscriptBox["z", "2"]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]]]

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

 2007-05-02