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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(17/4), 17/4, -(9/2), z] == (1/576) ((1/(1 - Sqrt[z])^(9/2)) (288 - 1296 Sqrt[z] + 3424 z - 7092 z^(3/2) + 12630 z^2 - 20337 z^(5/2) + 30312 z^3 - 42552 z^(7/2) + 56496 z^4 - 71280 z^(9/2) + 82368 z^5 - 72512 z^(11/2) + 38016 z^6 - 8448 z^(13/2)) + (1/(1 + Sqrt[z])^(9/2)) (288 + 1296 Sqrt[z] + 3424 z + 7092 z^(3/2) + 12630 z^2 + 20337 z^(5/2) + 30312 z^3 + 42552 z^(7/2) + 56496 z^4 + 71280 z^(9/2) + 82368 z^5 + 72512 z^(11/2) + 38016 z^6 + 8448 z^(13/2)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["17", "4"]]], ",", FractionBox["17", "4"], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "576"], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["9", "/", "2"]]]], RowBox[List["(", RowBox[List["288", "-", RowBox[List["1296", " ", SqrtBox["z"]]], "+", RowBox[List["3424", " ", "z"]], "-", RowBox[List["7092", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["12630", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["20337", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["30312", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["42552", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["56496", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["71280", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["82368", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["72512", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["38016", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["8448", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["9", "/", "2"]]]], RowBox[List["(", RowBox[List["288", "+", RowBox[List["1296", " ", SqrtBox["z"]]], "+", RowBox[List["3424", " ", "z"]], "+", RowBox[List["7092", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["12630", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["20337", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["30312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["42552", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["56496", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["71280", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["82368", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["72512", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["38016", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["8448", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 17 4 , 17 4 ; - 9 2 ; 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["17", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["17", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["9", "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] 1 576 ( 1 ( 1 - z ) 9 / 2 ( - 8448 z 13 / 2 + 38016 z 6 - 72512 z 11 / 2 + 82368 z 5 - 71280 z 9 / 2 + 56496 z 4 - 42552 z 7 / 2 + 30312 z 3 - 20337 z 5 / 2 + 12630 z 2 - 7092 z 3 / 2 + 3424 z - 1296 z + 288 ) + 1 ( z + 1 ) 9 / 2 ( 8448 z 13 / 2 + 38016 z 6 + 72512 z 11 / 2 + 82368 z 5 + 71280 z 9 / 2 + 56496 z 4 + 42552 z 7 / 2 + 30312 z 3 + 20337 z 5 / 2 + 12630 z 2 + 7092 z 3 / 2 + 3424 z + 1296 z + 288 ) ) HypergeometricPFQ -1 17 4 17 4 -1 9 2 z 1 576 1 1 -1 z 1 2 9 2 -1 -8448 z 13 2 38016 z 6 -1 72512 z 11 2 82368 z 5 -1 71280 z 9 2 56496 z 4 -1 42552 z 7 2 30312 z 3 -1 20337 z 5 2 12630 z 2 -1 7092 z 3 2 3424 z -1 1296 z 1 2 288 1 z 1 2 1 9 2 -1 8448 z 13 2 38016 z 6 72512 z 11 2 82368 z 5 71280 z 9 2 56496 z 4 42552 z 7 2 30312 z 3 20337 z 5 2 12630 z 2 7092 z 3 2 3424 z 1296 z 1 2 288 [/itex]

 Rule Form

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

 2007-05-02