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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a8xg.01

 Input Form

 Hypergeometric2F1[-(21/4), 21/4, 9/2, z] == (1/(1341153 z^(7/2))) (8 ((1 - Sqrt[z])^(9/2) (24 + 108 Sqrt[z] + 444 z + 1305 z^(3/2) + 4070 z^2 + 10692 z^(5/2) + 41184 z^3 + 208560 z^(7/2) + 434016 z^4 + 42240 z^(9/2) - 1081344 z^5 - 1613568 z^(11/2) - 963072 z^6 - 214016 z^(13/2)) + (1 + Sqrt[z])^(9/2) (-24 + 108 Sqrt[z] - 444 z + 1305 z^(3/2) - 4070 z^2 + 10692 z^(5/2) - 41184 z^3 + 208560 z^(7/2) - 434016 z^4 + 42240 z^(9/2) + 1081344 z^5 - 1613568 z^(11/2) + 963072 z^6 - 214016 z^(13/2))))

 Standard Form

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 MathML Form

 2 F 1 ( - 21 4 , 21 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["21", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[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 1341153 z 7 / 2 ( 8 ( ( - 214016 z 13 / 2 - 963072 z 6 - 1613568 z 11 / 2 - 1081344 z 5 + 42240 z 9 / 2 + 434016 z 4 + 208560 z 7 / 2 + 41184 z 3 + 10692 z 5 / 2 + 4070 z 2 + 1305 z 3 / 2 + 444 z + 108 z + 24 ) ( 1 - z ) 9 / 2 + ( z + 1 ) 9 / 2 ( - 214016 z 13 / 2 + 963072 z 6 - 1613568 z 11 / 2 + 1081344 z 5 + 42240 z 9 / 2 - 434016 z 4 + 208560 z 7 / 2 - 41184 z 3 + 10692 z 5 / 2 - 4070 z 2 + 1305 z 3 / 2 - 444 z + 108 z - 24 ) ) ) HypergeometricPFQ -1 21 4 21 4 9 2 z 1 1341153 z 7 2 -1 8 -214016 z 13 2 -1 963072 z 6 -1 1613568 z 11 2 -1 1081344 z 5 42240 z 9 2 434016 z 4 208560 z 7 2 41184 z 3 10692 z 5 2 4070 z 2 1305 z 3 2 444 z 108 z 1 2 24 1 -1 z 1 2 9 2 z 1 2 1 9 2 -214016 z 13 2 963072 z 6 -1 1613568 z 11 2 1081344 z 5 42240 z 9 2 -1 434016 z 4 208560 z 7 2 -1 41184 z 3 10692 z 5 2 -1 4070 z 2 1305 z 3 2 -1 444 z 108 z 1 2 -24 [/itex]

 Rule Form

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

 2007-05-02