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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ce0f.01

 Input Form

 Hypergeometric2F1[45/8, 47/8, 2, z] == (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-1 + z) (723695 + 68181412 z + 273739386 z^2 + 189230692 z^3 + 19610255 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 36 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-3618475 - 24588948 z - 28124994 z^2 - 5095188 z^3 + 151445 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (26197759 + 190676708 z + 257247834 z^2 + 74531492 z^3 + 2831647 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-1 + z) (723695 + 68181412 z + 273739386 z^2 + 189230692 z^3 + 19610255 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1044291885 Pi (-1 + z)^10 z)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["45", "8"], ",", FractionBox["47", "8"], ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["8", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["723695", "+", RowBox[List["68181412", " ", "z"]], "+", RowBox[List["273739386", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["189230692", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["19610255", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["36", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3618475"]], "-", RowBox[List["24588948", " ", "z"]], "-", RowBox[List["28124994", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5095188", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["151445", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["5", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["26197759", "+", RowBox[List["190676708", " ", "z"]], "+", RowBox[List["257247834", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["74531492", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2831647", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["723695", "+", RowBox[List["68181412", " ", "z"]], "+", RowBox[List["273739386", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["189230692", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["19610255", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["1044291885", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "10"], " ", "z"]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 45 8 , 47 8 ; 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["45", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["47", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["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 1044291885 π ( z - 1 ) 10 z ( 8 2 3 / 4 1 - z + 1 4 ( - 4 ( z - 1 ) ( 19610255 z 4 + 189230692 z 3 + 273739386 z 2 + 68181412 z + 723695 ) E ( 1 2 - 1 2 1 - z + 1 ) - 36 2 1 - z + 1 1 - z ( 151445 z 4 - 5095188 z 3 - 28124994 z 2 - 24588948 z - 3618475 ) K ( 1 2 - 1 2 1 - z + 1 ) + 5 2 1 - z + 1 ( z - 1 ) ( 2831647 z 4 + 74531492 z 3 + 257247834 z 2 + 190676708 z + 26197759 ) K ( 1 2 - 1 2 1 - z + 1 ) + 2 ( z - 1 ) ( 19610255 z 4 + 189230692 z 3 + 273739386 z 2 + 68181412 z + 723695 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 45 8 47 8 2 z 1 1044291885 z -1 10 z -1 8 2 3 4 1 -1 z 1 2 1 1 4 -4 z -1 19610255 z 4 189230692 z 3 273739386 z 2 68181412 z 723695 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 36 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 151445 z 4 -1 5095188 z 3 -1 28124994 z 2 -1 24588948 z -3618475 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 5 2 1 2 1 -1 z 1 2 1 1 2 z -1 2831647 z 4 74531492 z 3 257247834 z 2 190676708 z 26197759 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 2 z -1 19610255 z 4 189230692 z 3 273739386 z 2 68181412 z 723695 EllipticK 1 2 -1 1 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[FractionBox["45", "8"], ",", FractionBox["47", "8"], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["8", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["723695", "+", RowBox[List["68181412", " ", "z"]], "+", RowBox[List["273739386", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["189230692", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["19610255", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["36", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3618475"]], "-", RowBox[List["24588948", " ", "z"]], "-", RowBox[List["28124994", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5095188", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["151445", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["5", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["26197759", "+", RowBox[List["190676708", " ", "z"]], "+", RowBox[List["257247834", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["74531492", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2831647", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["723695", "+", RowBox[List["68181412", " ", "z"]], "+", RowBox[List["273739386", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["189230692", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["19610255", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["1044291885", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "10"], " ", "z"]]]]]]]

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

 2007-05-02