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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[5/2, 13/4, 2, z] == (2 Sqrt[2] (2 (1 + Sqrt[1 - z]) (1 - z)^(1/4) (10 + 197 z + 24 z^2) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (10 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) + (57 + 197 (1 - z)^(1/4) + 197 Sqrt[1 - z] + 197 (1 - z)^(3/4)) z + (-67 + 24 (1 - z)^(1/4) + 24 Sqrt[1 - z] + 24 (1 - z)^(3/4)) z^2) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (135 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^4 z)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "2"], ",", FractionBox["13", "4"], ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["197", " ", "z"]], "+", RowBox[List["24", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["10", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["57", "+", RowBox[List["197", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["197", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["197", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "67"]], "+", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["24", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["135", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "4"], " ", "z"]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 5 2 , 13 4 ; 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", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["13", "4"], 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] ( 2 2 ( 2 ( 1 - z + 1 ) 1 - z 4 ( 24 z 2 + 197 z + 10 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( ( 24 ( 1 - z ) 3 / 4 + 24 1 - z + 24 1 - z 4 - 67 ) z 2 + ( 197 ( 1 - z ) 3 / 4 + 197 1 - z + 197 1 - z 4 + 57 ) z + 10 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) / ( 135 π 1 - z + 1 ( z - 1 ) 4 z ) HypergeometricPFQ 5 2 13 4 2 z 2 2 1 2 2 1 -1 z 1 2 1 1 -1 z 1 4 24 z 2 197 z 10 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 24 1 -1 z 3 4 24 1 -1 z 1 2 24 1 -1 z 1 4 -67 z 2 197 1 -1 z 3 4 197 1 -1 z 1 2 197 1 -1 z 1 4 57 z 10 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 1 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 135 1 -1 z 1 2 1 1 2 z -1 4 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "2"], ",", FractionBox["13", "4"], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["197", " ", "z"]], "+", RowBox[List["24", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["10", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["57", "+", RowBox[List["197", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["197", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["197", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "67"]], "+", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["24", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]]]], ")"]]]], RowBox[List["135", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "4"], " ", "z"]]]]]]]

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

 2007-05-02