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; }

 BesselY

 http://functions.wolfram.com/03.03.06.0014.02

 Input Form

 BesselY[\[Nu], z] \[Proportional] (Csc[Pi \[Nu]]/Sqrt[2 Pi]) ((((z + I Sqrt[-z^2]) Cos[z + (1/4) Pi (1 - 2 \[Nu])])/ (E^(I Pi \[Nu]) (-z)^(3/2)) - ((z - I Sqrt[-z^2]) Cos[z + (1/4) Pi (-1 + 2 \[Nu])])/z^(3/2) + Cos[Pi \[Nu]] (((z - I Sqrt[-z^2]) Cos[z - (1/4) Pi (1 + 2 \[Nu])])/ z^(3/2) + (E^(I Pi \[Nu]) z (z + I Sqrt[-z^2]) Cos[z + (1/4) Pi (1 + 2 \[Nu])])/(-z)^(5/2))) HypergeometricPFQ[{1/4 - \[Nu]/2, 3/4 - \[Nu]/2, 1/4 + \[Nu]/2, 3/4 + \[Nu]/2}, {1/2}, -(1/z^2)] + ((1 - 4 \[Nu]^2)/(8 z)) (((z + I Sqrt[-z^2]) Sin[z + (1/4) Pi (1 - 2 \[Nu])])/ (E^(I Pi \[Nu]) (-z)^(3/2)) - ((z - I Sqrt[-z^2]) Sin[z + (1/4) Pi (-1 + 2 \[Nu])])/z^(3/2) + Cos[Pi \[Nu]] (((z - I Sqrt[-z^2]) Sin[z - (1/4) Pi (1 + 2 \[Nu])])/ z^(3/2) + (E^(I Pi \[Nu]) z (z + I Sqrt[-z^2]) Sin[z + (1/4) Pi (1 + 2 \[Nu])])/(-z)^(5/2))) HypergeometricPFQ[{3/4 - \[Nu]/2, 5/4 - \[Nu]/2, 3/4 + \[Nu]/2, 5/4 + \[Nu]/2}, {3/2}, -(1/z^2)]) /; (Abs[z] -> Infinity) && !Element[\[Nu], Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " "]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Pi]", " ", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "-", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]], " ", "z", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], RowBox[List["8", " ", "z", " "]]], RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Pi]", " ", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "-", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]], " ", "z", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "]"]]]]]]]]

 MathML Form

 Y ν ( z ) csc ( π ν ) 2 π ( ( cos ( π ν ) ( π ν z ( z + - z 2 ) ( - z ) 5 / 2 cos ( z + π ( 2 ν + 1 ) 4 ) + ( z - - z 2 ) z 3 / 2 cos ( z - π ( 2 ν + 1 ) 4 ) ) + - π ν ( z + - z 2 ) ( - z ) 3 / 2 cos ( z + π ( 1 - 2 ν ) 4 ) - ( z - - z 2 ) z 3 / 2 cos ( z + π ( 2 ν - 1 ) 4 ) ) 4 F 1 ( 1 4 - ν 2 , 3 4 - ν 2 , ν 2 + 1 4 , ν 2 + 3 4 TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; 1 2 TagBox[TagBox[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; - 1 z 2 TagBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]] ) + 1 - 4 ν 2 8 z ( cos ( π ν ) ( π ν z ( z + - z 2 ) ( - z ) 5 / 2 sin ( z + π ( 2 ν + 1 ) 4 ) + ( z - - z 2 ) z 3 / 2 sin ( z - π ( 2 ν + 1 ) 4 ) ) + - π ν ( z + - z 2 ) ( - z ) 3 / 2 sin ( z + π ( 1 - 2 ν ) 4 ) - ( z - - z 2 ) z 3 / 2 sin ( z + π ( 2 ν - 1 ) 4 ) ) 4 F 1 ( 3 4 - ν 2 , 5 4 - ν 2 , ν 2 + 3 4 , ν 2 + 5 4 TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["5", "4"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["5", "4"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; 3 2 TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; - 1 z 2 TagBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]] ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) ν TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] FormBox RowBox RowBox RowBox SubscriptBox Y ν ( z ) RowBox FractionBox RowBox csc ( RowBox π ν ) SqrtBox RowBox 2 π RowBox ( RowBox RowBox RowBox ( RowBox RowBox RowBox cos ( RowBox π ν ) RowBox ( RowBox RowBox FractionBox RowBox SuperscriptBox RowBox π ν z RowBox ( RowBox z + RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox RowBox ( RowBox - z ) RowBox 5 / 2 RowBox cos ( RowBox z + FractionBox RowBox π RowBox ( RowBox RowBox 2 ν + 1 ) 4 ) + RowBox FractionBox RowBox ( RowBox z - RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox z RowBox 3 / 2 RowBox cos ( RowBox z - FractionBox RowBox π RowBox ( RowBox RowBox 2 ν + 1 ) 4 ) ) + RowBox FractionBox RowBox SuperscriptBox RowBox RowBox - π ν RowBox ( RowBox z + RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox RowBox ( RowBox - z ) RowBox 3 / 2 RowBox cos ( RowBox z + FractionBox RowBox π RowBox ( RowBox 1 - RowBox 2 ν ) 4 ) - RowBox FractionBox RowBox ( RowBox z - RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox z RowBox 3 / 2 RowBox cos ( RowBox z + FractionBox RowBox π RowBox ( RowBox RowBox 2 ν - 1 ) 4 ) ) RowBox RowBox SubscriptBox ErrorBox FormBox 4 TraditionalForm SubscriptBox F FormBox 1 TraditionalForm RowBox ( RowBox TagBox TagBox RowBox TagBox RowBox FractionBox 1 4 - FractionBox ν 2 HypergeometricPFQ Rule Editable , TagBox RowBox FractionBox 3 4 - FractionBox ν 2 HypergeometricPFQ Rule Editable , TagBox RowBox FractionBox ν 2 + FractionBox 1 4 HypergeometricPFQ Rule Editable , TagBox RowBox FractionBox ν 2 + FractionBox 3 4 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox TagBox TagBox FractionBox 1 2 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox RowBox - FractionBox 1 SuperscriptBox z 2 HypergeometricPFQ Rule Editable ) + RowBox FractionBox RowBox 1 - RowBox 4 SuperscriptBox ν 2 RowBox 8 z RowBox ( RowBox RowBox RowBox cos ( RowBox π ν ) RowBox ( RowBox RowBox FractionBox RowBox SuperscriptBox RowBox π ν z RowBox ( RowBox z + RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox RowBox ( RowBox - z ) RowBox 5 / 2 RowBox sin ( RowBox z + FractionBox RowBox π RowBox ( RowBox RowBox 2 ν + 1 ) 4 ) + RowBox FractionBox RowBox ( RowBox z - RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox z RowBox 3 / 2 RowBox sin ( RowBox z - FractionBox RowBox π RowBox ( RowBox RowBox 2 ν + 1 ) 4 ) ) + RowBox FractionBox RowBox SuperscriptBox RowBox RowBox - π ν RowBox ( RowBox z + RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox RowBox ( RowBox - z ) RowBox 3 / 2 RowBox sin ( RowBox z + FractionBox RowBox π RowBox ( RowBox 1 - RowBox 2 ν ) 4 ) - RowBox FractionBox RowBox ( RowBox z - RowBox SqrtBox RowBox - SuperscriptBox z 2 ) SuperscriptBox z RowBox 3 / 2 RowBox sin ( RowBox z + FractionBox RowBox π RowBox ( RowBox RowBox 2 ν - 1 ) 4 ) ) RowBox RowBox SubscriptBox FormBox 4 TraditionalForm SubscriptBox F FormBox 1 TraditionalForm RowBox ( RowBox TagBox TagBox RowBox TagBox RowBox FractionBox 3 4 - FractionBox ν 2 HypergeometricPFQ Rule Editable , TagBox RowBox FractionBox 5 4 - FractionBox ν 2 HypergeometricPFQ Rule Editable , TagBox RowBox FractionBox ν 2 + FractionBox 3 4 HypergeometricPFQ Rule Editable , TagBox RowBox FractionBox ν 2 + FractionBox 5 4 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox TagBox TagBox FractionBox 3 2 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox RowBox - FractionBox 1 SuperscriptBox z 2 HypergeometricPFQ Rule Editable ) ) /; RowBox RowBox ( RowBox RowBox z ) RowBox ν TagBox Function TraditionalForm [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Pi]", " ", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "-", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]], " ", "z", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Pi]", " ", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "-", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]], " ", "z", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["z", "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "4"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]]]], RowBox[List["8", " ", "z"]]]]], ")"]]]], SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]]]]

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

 2001-10-29