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 KelvinKei

 http://functions.wolfram.com/03.19.22.0001.01

 Input Form

 LaplaceTransform[KelvinKei[\[Nu], t], t, z] == 2^(-3 - \[Nu]) Pi z^(-3 - \[Nu]) Csc[Pi \[Nu]] (z^(2 \[Nu]) (2^(1 + 2 \[Nu]) - 4^\[Nu] \[Nu]) Cos[(3 Pi \[Nu])/4] HypergeometricPFQ[{3/4 - \[Nu]/4, 1 - \[Nu]/4, 5/4 - \[Nu]/4, 3/2 - \[Nu]/4}, {3/2, 1 - \[Nu]/2, 3/2 - \[Nu]/2}, -(1/z^4)] - (2 + \[Nu]) Cos[(Pi \[Nu])/4] HypergeometricPFQ[ {3/4 + \[Nu]/4, 1 + \[Nu]/4, 5/4 + \[Nu]/4, 3/2 + \[Nu]/4}, {3/2, 1 + \[Nu]/2, 3/2 + \[Nu]/2}, -(1/z^4)] + 4 z^2 (Sin[(Pi \[Nu])/4] HypergeometricPFQ[{1/4 + \[Nu]/4, 1/2 + \[Nu]/4, 3/4 + \[Nu]/4, 1 + \[Nu]/4}, {1/2, 1/2 + \[Nu]/2, 1 + \[Nu]/2}, -(1/z^4)] - 4^\[Nu] z^(2 \[Nu]) Sin[(3 Pi \[Nu])/4] HypergeometricPFQ[{1/4 - \[Nu]/4, 1/2 - \[Nu]/4, 3/4 - \[Nu]/4, 1 - \[Nu]/4}, {1/2, 1/2 - \[Nu]/2, 1 - \[Nu]/2}, -(1/z^4)])) /; Abs[Re[\[Nu]]] < 1 && Re[z] > -(1/Sqrt[2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaplaceTransform", "[", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "t"]], "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "\[Nu]"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "-", "\[Nu]"]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]]], "-", RowBox[List[SuperscriptBox["4", "\[Nu]"], " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["4", "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "\[Nu]", "]"]], "]"]], "<", "1"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", RowBox[List["-", FractionBox["1", SqrtBox["2"]]]]]]]]]]]]

 MathML Form

 t [ kei ν ( t ) ] ( z ) 2 - ν - 3 π z - ν - 3 csc ( π ν ) ( ( 2 2 ν + 1 - 4 ν ν ) cos ( 3 π ν 4 ) z 2 ν 4 F 3 ( 3 4 - ν 4 , 1 - ν 4 , 5 4 - ν 4 , 3 2 - ν 4 ; 3 2 , 1 - ν 2 , 3 2 - ν 2 ; - 1 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["5", "4"], "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] + 4 ( sin ( π ν 4 ) 4 F 3 ( ν 4 + 1 4 , ν 4 + 1 2 , ν 4 + 3 4 , ν 4 + 1 ; 1 2 , ν 2 + 1 2 , ν 2 + 1 ; - 1 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 4 ν z 2 ν sin ( 3 π ν 4 ) 4 F 3 ( 1 4 - ν 4 , 1 2 - ν 4 , 3 4 - ν 4 , 1 - ν 4 ; 1 2 , 1 2 - ν 2 , 1 - ν 2 ; - 1 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ) z 2 - ( ν + 2 ) cos ( π ν 4 ) 4 F 3 ( ν 4 + 3 4 , ν 4 + 1 , ν 4 + 5 4 , ν 4 + 3 2 ; 3 2 , ν 2 + 1 , ν 2 + 3 2 ; - 1 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", FractionBox["5", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "4"], "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ) /; "\[LeftBracketingBar]" Re ( ν ) "\[RightBracketingBar]" < 1 Re ( z ) > - 1 2 Condition LaplaceTransform KelvinKei ν t t z 2 -1 ν -3 z -1 ν -3 ν 2 2 ν 1 -1 4 ν ν 3 ν 4 -1 z 2 ν HypergeometricPFQ 3 4 -1 ν 4 -1 1 -1 ν 4 -1 5 4 -1 ν 4 -1 3 2 -1 ν 4 -1 3 2 1 -1 ν 2 -1 3 2 -1 ν 2 -1 -1 1 z 4 -1 4 ν 4 -1 HypergeometricPFQ ν 4 -1 1 4 ν 4 -1 1 2 ν 4 -1 3 4 ν 4 -1 1 1 2 ν 2 -1 1 2 ν 2 -1 1 -1 1 z 4 -1 -1 4 ν z 2 ν 3 ν 4 -1 HypergeometricPFQ 1 4 -1 ν 4 -1 1 2 -1 ν 4 -1 3 4 -1 ν 4 -1 1 -1 ν 4 -1 1 2 1 2 -1 ν 2 -1 1 -1 ν 2 -1 -1 1 z 4 -1 z 2 -1 ν 2 ν 4 -1 HypergeometricPFQ ν 4 -1 3 4 ν 4 -1 1 ν 4 -1 5 4 ν 4 -1 3 2 3 2 ν 2 -1 1 ν 2 -1 3 2 -1 1 z 4 -1 ν 1 z -1 1 2 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaplaceTransform", "[", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", "t_"]], "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "\[Nu]"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "-", "\[Nu]"]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]]], "-", RowBox[List[SuperscriptBox["4", "\[Nu]"], " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["4", "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Nu]", "4"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "\[Nu]", "]"]], "]"]], "<", "1"]], "&&", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", RowBox[List["-", FractionBox["1", SqrtBox["2"]]]]]]]]]]]]]]

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

 2007-05-02