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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b4ts.01

 Input Form

 Hypergeometric2F1[-(47/8), -(19/8), 1, z] == (2 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (7734685009 + 66543867524 z + 66899859534 z^2 + 1076474564 z^3 - 139386071 z^4 + 10483440 z^5) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (7734685009 + 66543867524 z + 66899859534 z^2 + 1076474564 z^3 - 139386071 z^4 + 10483440 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (7734685009 + 66543867524 z + 66899859534 z^2 + 1076474564 z^3 - 139386071 z^4 + 10483440 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-912750313 - 34502107520 z - 85841349030 z^2 - 22886223140 z^3 + 2284297895 z^4 - 288818772 z^5 + 20966880 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (9560185635 Pi (1 + Sqrt[1 - z])^(1/4))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["47", "8"]]], ",", RowBox[List["-", FractionBox["19", "8"]]], ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["7734685009", "+", RowBox[List["66543867524", " ", "z"]], "+", RowBox[List["66899859534", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1076474564", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["139386071", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["10483440", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["7734685009", "+", RowBox[List["66543867524", " ", "z"]], "+", RowBox[List["66899859534", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1076474564", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["139386071", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["10483440", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["7734685009", "+", RowBox[List["66543867524", " ", "z"]], "+", RowBox[List["66899859534", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1076474564", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["139386071", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["10483440", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "912750313"]], "-", RowBox[List["34502107520", " ", "z"]], "-", RowBox[List["85841349030", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["22886223140", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2284297895", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["288818772", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["20966880", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["9560185635", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 47 8 , - 19 8 ; 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["47", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["19", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["1", 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 9560185635 π 1 - z + 1 4 ( 2 2 4 ( 2 2 1 - z + 1 1 - z 4 ( 10483440 z 5 - 139386071 z 4 + 1076474564 z 3 + 66899859534 z 2 + 66543867524 z + 7734685009 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - 1 - z ( 10483440 z 5 - 139386071 z 4 + 1076474564 z 3 + 66899859534 z 2 + 66543867524 z + 7734685009 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) - 2 1 - z + 1 1 - z 4 ( 10483440 z 5 - 139386071 z 4 + 1076474564 z 3 + 66899859534 z 2 + 66543867524 z + 7734685009 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) - 2 ( 20966880 z 6 - 288818772 z 5 + 2284297895 z 4 - 22886223140 z 3 - 85841349030 z 2 - 34502107520 z - 912750313 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) HypergeometricPFQ -1 47 8 -1 19 8 1 z 1 9560185635 1 -1 z 1 2 1 1 4 -1 2 2 1 4 2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 10483440 z 5 -1 139386071 z 4 1076474564 z 3 66899859534 z 2 66543867524 z 7734685009 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 1 -1 z 1 2 10483440 z 5 -1 139386071 z 4 1076474564 z 3 66899859534 z 2 66543867524 z 7734685009 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 10483440 z 5 -1 139386071 z 4 1076474564 z 3 66899859534 z 2 66543867524 z 7734685009 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 2 20966880 z 6 -1 288818772 z 5 2284297895 z 4 -1 22886223140 z 3 -1 85841349030 z 2 -1 34502107520 z -912750313 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["47", "8"]]], ",", RowBox[List["-", FractionBox["19", "8"]]], ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["7734685009", "+", RowBox[List["66543867524", " ", "z"]], "+", RowBox[List["66899859534", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1076474564", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["139386071", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["10483440", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["7734685009", "+", RowBox[List["66543867524", " ", "z"]], "+", RowBox[List["66899859534", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1076474564", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["139386071", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["10483440", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["7734685009", "+", RowBox[List["66543867524", " ", "z"]], "+", RowBox[List["66899859534", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1076474564", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["139386071", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["10483440", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "912750313"]], "-", RowBox[List["34502107520", " ", "z"]], "-", RowBox[List["85841349030", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["22886223140", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2284297895", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["288818772", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["20966880", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["9560185635", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]]

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

 2007-05-02