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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ako7.01

 Input Form

 Hypergeometric2F1[7/4, 19/4, 1, -z] == (1/(1155 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (-(((-1117 + 738 z + 207 z^2 + 32 z^3) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^5) - ((-1117 + 738 z + 207 z^2 + 32 z^3) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^(9/2) + (2 (19 - 1638 z + 27 z^2 + 4 z^3) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^(11/2) + ((-1117 + 738 z + 207 z^2 + 32 z^3) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^5))

 Standard Form

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 MathML Form

 2 F 1 ( 7 4 , 19 4 ; 1 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["19", "4"], 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[RowBox[List["-", "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 1155 π z + 1 + 1 ( 2 2 ( - ( 32 z 3 + 207 z 2 + 738 z - 1117 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 9 / 2 - ( 32 z 3 + 207 z 2 + 738 z - 1117 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 + 2 ( 4 z 3 + 27 z 2 - 1638 z + 19 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 11 / 2 + ( 32 z 3 + 207 z 2 + 738 z - 1117 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 ) ) HypergeometricPFQ 7 4 19 4 1 -1 z 1 1155 z 1 1 2 1 1 2 -1 2 2 1 2 -1 32 z 3 207 z 2 738 z -1117 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 9 2 -1 -1 32 z 3 207 z 2 738 z -1117 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 2 4 z 3 27 z 2 -1 1638 z 19 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 11 2 -1 32 z 3 207 z 2 738 z -1117 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["7", "4"], ",", FractionBox["19", "4"], ",", "1", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1117"]], "+", RowBox[List["738", " ", "z"]], "+", RowBox[List["207", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "5"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1117"]], "+", RowBox[List["738", " ", "z"]], "+", RowBox[List["207", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["9", "/", "2"]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["19", "-", RowBox[List["1638", " ", "z"]], "+", RowBox[List["27", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["11", "/", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1117"]], "+", RowBox[List["738", " ", "z"]], "+", RowBox[List["207", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "5"]]]], ")"]]]], RowBox[List["1155", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]]]]]

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

 2007-05-02