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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.al35.01

 Input Form

 Hypergeometric2F1[9/4, 9/4, 21/4, z] == (1/(40960 z^(17/4))) (1989 (72 (1 - z)^(3/4) z^(1/4) (-65 + 28 z) - 10 Sqrt[2] (117 - 144 z + 32 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 10 Sqrt[2] (117 - 144 z + 32 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 5 Sqrt[2] (117 - 144 z + 32 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 5 Sqrt[2] (117 - 144 z + 32 z^2) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))

 Standard Form

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 MathML Form

 2 F 1 ( 9 4 , 9 4 ; 21 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["9", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["21", "4"], 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 40960 z 17 / 4 ( 1989 ( 72 ( 1 - z ) 3 / 4 z 4 ( 28 z - 65 ) - 10 2 ( 32 z 2 - 144 z + 117 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) - 10 2 ( 32 z 2 - 144 z + 117 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) - 5 2 ( 32 z 2 - 144 z + 117 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) + 5 2 ( 32 z 2 - 144 z + 117 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) ) HypergeometricPFQ 9 4 9 4 21 4 z 1 40960 z 17 4 -1 1989 72 1 -1 z 3 4 z 1 4 28 z -65 -1 10 2 1 2 32 z 2 -1 144 z 117 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 10 2 1 2 32 z 2 -1 144 z 117 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 5 2 1 2 32 z 2 -1 144 z 117 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 5 2 1 2 32 z 2 -1 144 z 117 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 [/itex]

 Rule Form

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

 2007-05-02