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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ajzm.01

 Input Form

 Hypergeometric2F1[5/4, 17/4, 9/2, z] == (1/(1755 Pi^(3/2) z^(7/2))) (112 (-((2 (-120 + 24 z + 19 z^2 + 32 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)) + (2 (-120 + 24 z + 19 z^2 + 32 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z) + ((-120 + 60 Sqrt[z] - 36 z + 43 z^(3/2) - 24 z^2 + 32 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])])/(-1 + Sqrt[z]) - ((120 + 60 Sqrt[z] + 36 z + 43 z^(3/2) + 24 z^2 + 32 z^(5/2)) EllipticK[(1/2) (1 + Sqrt[z])])/(1 + Sqrt[z])) Gamma[3/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "4"], ",", FractionBox["17", "4"], ",", FractionBox["9", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1755", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]], RowBox[List["(", RowBox[List["112", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120"]], "+", RowBox[List["24", " ", "z"]], "+", RowBox[List["19", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120"]], "+", RowBox[List["24", " ", "z"]], "+", RowBox[List["19", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "120"]], "+", RowBox[List["60", " ", SqrtBox["z"]]], "-", RowBox[List["36", " ", "z"]], "+", RowBox[List["43", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["120", "+", RowBox[List["60", " ", SqrtBox["z"]]], "+", RowBox[List["36", " ", "z"]], "+", RowBox[List["43", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List["1", "+", SqrtBox["z"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 5 4 , 17 4 ; 9 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["17", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["9", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 1755 π 3 / 2 z 7 / 2 ( 112 ( - 2 ( 32 z 3 + 19 z 2 + 24 z - 120 ) E ( 1 2 ( 1 - z ) ) z - 1 + 2 ( 32 z 3 + 19 z 2 + 24 z - 120 ) E ( 1 2 ( z + 1 ) ) z - 1 + ( 32 z 5 / 2 - 24 z 2 + 43 z 3 / 2 - 36 z + 60 z - 120 ) K ( 1 2 ( 1 - z ) ) z - 1 - ( 32 z 5 / 2 + 24 z 2 + 43 z 3 / 2 + 36 z + 60 z + 120 ) K ( 1 2 ( z + 1 ) ) z + 1 ) Γ ( 3 4 ) 2 ) HypergeometricPFQ 5 4 17 4 9 2 z 1 1755 3 2 z 7 2 -1 112 -1 2 32 z 3 19 z 2 24 z -120 EllipticE 1 2 1 -1 z 1 2 z -1 -1 2 32 z 3 19 z 2 24 z -120 EllipticE 1 2 z 1 2 1 z -1 -1 32 z 5 2 -1 24 z 2 43 z 3 2 -1 36 z 60 z 1 2 -120 EllipticK 1 2 1 -1 z 1 2 z 1 2 -1 -1 -1 32 z 5 2 24 z 2 43 z 3 2 36 z 60 z 1 2 120 EllipticK 1 2 z 1 2 1 z 1 2 1 -1 Gamma 3 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "4"], ",", FractionBox["17", "4"], ",", FractionBox["9", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["112", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120"]], "+", RowBox[List["24", " ", "z"]], "+", RowBox[List["19", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120"]], "+", RowBox[List["24", " ", "z"]], "+", RowBox[List["19", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "120"]], "+", RowBox[List["60", " ", SqrtBox["z"]]], "-", RowBox[List["36", " ", "z"]], "+", RowBox[List["43", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["120", "+", RowBox[List["60", " ", SqrtBox["z"]]], "+", RowBox[List["36", " ", "z"]], "+", RowBox[List["43", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List["1", "+", SqrtBox["z"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["1755", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]]]]]

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

 2007-05-02