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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.cc9j.01

 Input Form

 Hypergeometric2F1[33/8, 45/8, 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1664 - 11895 z + 45435 z^2 + 385375 z^3 + 765 z^4) 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) (1664 - 11895 z + 45435 z^2 + 385375 z^3 + 765 z^4) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (1664 - 11895 z + 45435 z^2 + 385375 z^3 + 765 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-1 + z) (-1664 + 10855 z - 38870 z^2 - 43605 z^3 + 3060 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (373484475 Pi (1 + Sqrt[1 - z])^(1/4) (-1 + z)^6 z^3)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["33", "8"], ",", FractionBox["45", "8"], ",", "4", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["2048", " ", 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["1664", "-", RowBox[List["11895", " ", "z"]], "+", RowBox[List["45435", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["385375", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1664", "-", RowBox[List["11895", " ", "z"]], "+", RowBox[List["45435", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["385375", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1664", "-", RowBox[List["11895", " ", "z"]], "+", RowBox[List["45435", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["385375", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1664"]], "+", RowBox[List["10855", " ", "z"]], "-", RowBox[List["38870", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["43605", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3060", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["373484475", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"], " ", SuperscriptBox["z", "3"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 33 8 , 45 8 ; 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["33", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["45", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["4", 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] ( 2048 2 4 ( 2 2 1 - z + 1 1 - z 4 ( 765 z 4 + 385375 z 3 + 45435 z 2 - 11895 z + 1664 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - 1 - z ( 765 z 4 + 385375 z 3 + 45435 z 2 - 11895 z + 1664 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) - 2 1 - z + 1 1 - z 4 ( 765 z 4 + 385375 z 3 + 45435 z 2 - 11895 z + 1664 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) - ( z - 1 ) ( 3060 z 4 - 43605 z 3 - 38870 z 2 + 10855 z - 1664 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) / ( 373484475 π 1 - z + 1 4 ( z - 1 ) 6 z 3 ) HypergeometricPFQ 33 8 45 8 4 z 2048 2 1 4 2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 765 z 4 385375 z 3 45435 z 2 -1 11895 z 1664 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 2 765 z 4 385375 z 3 45435 z 2 -1 11895 z 1664 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 4 765 z 4 385375 z 3 45435 z 2 -1 11895 z 1664 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 z -1 3060 z 4 -1 43605 z 3 -1 38870 z 2 10855 z -1664 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 373484475 1 -1 z 1 2 1 1 4 z -1 6 z 3 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["33", "8"], ",", FractionBox["45", "8"], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2048", " ", 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["1664", "-", RowBox[List["11895", " ", "z"]], "+", RowBox[List["45435", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["385375", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1664", "-", RowBox[List["11895", " ", "z"]], "+", RowBox[List["45435", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["385375", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1664", "-", RowBox[List["11895", " ", "z"]], "+", RowBox[List["45435", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["385375", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1664"]], "+", RowBox[List["10855", " ", "z"]], "-", RowBox[List["38870", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["43605", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3060", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["373484475", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"], " ", SuperscriptBox["z", "3"]]]]]]]]

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

 2007-05-02