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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ai6n.01

 Input Form

 Hypergeometric2F1[1/4, 9/4, 21/4, z] == (1/(524288 z^(17/4))) (663 (-8 (1 - z)^(3/4) z^(1/4) (585 - 972 z + 224 z^2 + 128 z^3) - 30 Sqrt[2] (39 - 96 z + 64 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 30 Sqrt[2] (39 - 96 z + 64 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 15 Sqrt[2] (39 - 96 z + 64 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 15 Sqrt[2] (39 - 96 z + 64 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 ( 1 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["1", "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 524288 z 17 / 4 ( 663 ( - 8 ( 1 - z ) 3 / 4 z 4 ( 128 z 3 + 224 z 2 - 972 z + 585 ) - 30 2 ( 64 z 2 - 96 z + 39 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) - 30 2 ( 64 z 2 - 96 z + 39 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) - 15 2 ( 64 z 2 - 96 z + 39 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) + 15 2 ( 64 z 2 - 96 z + 39 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) ) HypergeometricPFQ 1 4 9 4 21 4 z 1 524288 z 17 4 -1 663 -8 1 -1 z 3 4 z 1 4 128 z 3 224 z 2 -1 972 z 585 -1 30 2 1 2 64 z 2 -1 96 z 39 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 30 2 1 2 64 z 2 -1 96 z 39 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 15 2 1 2 64 z 2 -1 96 z 39 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 15 2 1 2 64 z 2 -1 96 z 39 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