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 KelvinBer

 http://functions.wolfram.com/03.18.06.0053.01

 Input Form

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

 Standard Form

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"\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]]], 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["\[ImaginaryI]", SuperscriptBox["z", "2"]]]]]], "]"]]]], " ", "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]], " ", 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"4"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]]]], "]"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]]], 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"], "}"]], ",", FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]], "+", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], "z"], RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], "-", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]], 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["\[ImaginaryI]", SuperscriptBox["z", "2"]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 ber ν ( z ) - 1 4 - 1 4 ( π ν ) z ν 2 2 π ( ( z 2 ( z 2 + 3 π ν 2 ( ( - 1 ) 3 / 4 z ) - ν - 1 2 4 F 1 ( 1 4 - ν 2 , 3 4 - ν 2 , ν 2 + 1 4 , ν 2 + 3 4 ; 1 2 ; - z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - - z 2 ( - - 1 4 z ) - ν - 1 2 ( ( ( - 1 ) 3 / 4 - z 2 ) cos ( π ν ) z + sin ( π ν ) ) 4 F 1 ( 1 4 - ν 2 , 3 4 - ν 2 , ν 2 + 1 4 , ν 2 + 3 4 ; 1 2 ; z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) + - z 2 ( z 2 ( - - 1 4 z ) - ν - 1 2 4 F 1 ( 1 4 - ν 2 , 3 4 - ν 2 , ν 2 + 1 4 , ν 2 + 3 4 ; 1 2 ; z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + 3 π ν 2 - z 2 ( ( - 1 ) 3 / 4 z ) - ν - 1 2 ( - 1 4 z 2 z cos ( π ν ) - sin ( π ν ) ) 4 F 1 ( 1 4 - ν 2 , 3 4 - ν 2 , ν 2 + 1 4 , ν 2 + 3 4 ; 1 2 ; - z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) ) + ( - 1 ) 3 / 4 ( 1 - 4 ν 2 ) 8 z ( z 2 ( - z 2 ( - - 1 4 z ) - ν - 1 2 ( ( - 1 ) 3 / 4 - z 2 z cos ( π ν ) + sin ( π ν ) ) 4 F 1 ( 3 4 - ν 2 , 5 4 - ν 2 , ν 2 + 3 4 , ν 2 + 5 4 ; 3 2 ; z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - z 2 + 3 π ν 2 ( ( - 1 ) 3 / 4 z ) - ν - 1 2 4 F 1 ( 3 4 - ν 2 , 5 4 - ν 2 , ν 2 + 3 4 , ν 2 + 5 4 ; 3 2 ; - z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) + - z 2 ( z 2 ( - - 1 4 z ) - ν - 1 2 4 F 1 ( 3 4 - ν 2 , 5 4 - ν 2 , ν 2 + 3 4 , ν 2 + 5 4 ; 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3 2 ; - z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["\[ImaginaryI]", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinBer ν z -1 1 4 -1 1 4 ν z ν 2 2 1 2 -1 z 2 1 2 -1 z 2 1 2 -1 3 ν 2 -1 -1 3 4 z -1 ν -1 1 2 HypergeometricPFQ 1 4 -1 ν 2 -1 3 4 -1 ν 2 -1 ν 2 -1 1 4 ν 2 -1 3 4 1 2 -1 z 2 -1 -1 -1 z 2 1 2 -1 -1 -1 1 4 z -1 ν -1 1 2 -1 3 4 -1 z 2 1 2 ν z -1 ν HypergeometricPFQ 1 4 -1 ν 2 -1 3 4 -1 ν 2 -1 ν 2 -1 1 4 ν 2 -1 3 4 1 2 z 2 -1 -1 z 2 1 2 -1 z 2 1 2 -1 -1 -1 1 4 z -1 ν -1 1 2 HypergeometricPFQ 1 4 -1 ν 2 -1 3 4 -1 ν 2 -1 ν 2 -1 1 4 ν 2 -1 3 4 1 2 z 2 -1 3 ν 2 -1 -1 z 2 1 2 -1 -1 3 4 z -1 ν -1 1 2 -1 1 4 z 2 1 2 z -1 ν -1 ν HypergeometricPFQ 1 4 -1 ν 2 -1 3 4 -1 ν 2 -1 ν 2 -1 1 4 ν 2 -1 3 4 1 2 -1 z 2 -1 -1 3 4 1 -1 4 ν 2 8 z -1 z 2 1 2 -1 -1 z 2 1 2 -1 -1 -1 1 4 z -1 ν -1 1 2 -1 3 4 -1 z 2 1 2 z -1 ν ν HypergeometricPFQ 3 4 -1 ν 2 -1 5 4 -1 ν 2 -1 ν 2 -1 3 4 ν 2 -1 5 4 3 2 z 2 -1 -1 z 2 1 2 -1 3 ν 2 -1 -1 3 4 z -1 ν -1 1 2 HypergeometricPFQ 3 4 -1 ν 2 -1 5 4 -1 ν 2 -1 ν 2 -1 3 4 ν 2 -1 5 4 3 2 -1 z 2 -1 -1 z 2 1 2 -1 z 2 1 2 -1 -1 -1 1 4 z -1 ν -1 1 2 HypergeometricPFQ 3 4 -1 ν 2 -1 5 4 -1 ν 2 -1 ν 2 -1 3 4 ν 2 -1 5 4 3 2 z 2 -1 3 ν 2 -1 -1 z 2 1 2 -1 -1 3 4 z -1 ν -1 1 2 -1 1 4 z 2 1 2 z -1 ν -1 ν HypergeometricPFQ 3 4 -1 ν 2 -1 5 4 -1 ν 2 -1 ν 2 -1 3 4 ν 2 -1 5 4 3 2 -1 z 2 -1 Rule z [/itex]

 Rule Form

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

 2007-05-02