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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a9ks.01

 Input Form

 Hypergeometric2F1[-(19/4), 11/4, -(11/2), z] == (1/2688) ((1/(1 - Sqrt[z])^(7/2)) (1344 - 4704 Sqrt[z] + 9072 z - 14112 z^(3/2) + 19320 z^2 - 24402 z^(5/2) + 28907 z^3 - 32536 z^(7/2) + 34776 z^4 - 35280 z^(9/2) + 33264 z^5 - 28224 z^(11/2) + 17472 z^6 - 4992 z^(13/2)) + (1/(1 + Sqrt[z])^(7/2)) (1344 + 4704 Sqrt[z] + 9072 z + 14112 z^(3/2) + 19320 z^2 + 24402 z^(5/2) + 28907 z^3 + 32536 z^(7/2) + 34776 z^4 + 35280 z^(9/2) + 33264 z^5 + 28224 z^(11/2) + 17472 z^6 + 4992 z^(13/2)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["19", "4"]]], ",", FractionBox["11", "4"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2688"], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["7", "/", "2"]]]], RowBox[List["(", RowBox[List["1344", "-", RowBox[List["4704", " ", SqrtBox["z"]]], "+", RowBox[List["9072", " ", "z"]], "-", RowBox[List["14112", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["19320", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["24402", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["28907", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["32536", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["34776", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["35280", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["33264", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["28224", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["17472", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["4992", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["7", "/", "2"]]]], RowBox[List["(", RowBox[List["1344", "+", RowBox[List["4704", " ", SqrtBox["z"]]], "+", RowBox[List["9072", " ", "z"]], "+", RowBox[List["14112", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["19320", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["24402", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["28907", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["32536", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["34776", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["35280", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["33264", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["28224", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["17472", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["4992", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 19 4 , 11 4 ; - 11 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["19", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "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["11", "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 2688 ( 1 ( 1 - z ) 7 / 2 ( - 4992 z 13 / 2 + 17472 z 6 - 28224 z 11 / 2 + 33264 z 5 - 35280 z 9 / 2 + 34776 z 4 - 32536 z 7 / 2 + 28907 z 3 - 24402 z 5 / 2 + 19320 z 2 - 14112 z 3 / 2 + 9072 z - 4704 z + 1344 ) + 1 ( z + 1 ) 7 / 2 ( 4992 z 13 / 2 + 17472 z 6 + 28224 z 11 / 2 + 33264 z 5 + 35280 z 9 / 2 + 34776 z 4 + 32536 z 7 / 2 + 28907 z 3 + 24402 z 5 / 2 + 19320 z 2 + 14112 z 3 / 2 + 9072 z + 4704 z + 1344 ) ) HypergeometricPFQ -1 19 4 11 4 -1 11 2 z 1 2688 1 1 -1 z 1 2 7 2 -1 -4992 z 13 2 17472 z 6 -1 28224 z 11 2 33264 z 5 -1 35280 z 9 2 34776 z 4 -1 32536 z 7 2 28907 z 3 -1 24402 z 5 2 19320 z 2 -1 14112 z 3 2 9072 z -1 4704 z 1 2 1344 1 z 1 2 1 7 2 -1 4992 z 13 2 17472 z 6 28224 z 11 2 33264 z 5 35280 z 9 2 34776 z 4 32536 z 7 2 28907 z 3 24402 z 5 2 19320 z 2 14112 z 3 2 9072 z 4704 z 1 2 1344 [/itex]

 Rule Form

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

 2007-05-02