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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.al1w.01

 Input Form

 Hypergeometric2F1[2, 6, -(1/4), z] == (1/262144) ((8 (32768 - 1835008 z - 7475455 z^2 - 1014960 z^3 + 240720 z^4 - 46848 z^5 + 4608 z^6))/(-1 + z)^8 + (696150 Sqrt[2] z^(5/4) (9 + 20 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(33/4) + (696150 Sqrt[2] z^(5/4) (9 + 20 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(33/4) - (348075 Sqrt[2] z^(5/4) (9 + 20 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(33/4) + (348075 Sqrt[2] z^(5/4) (9 + 20 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(33/4))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 6 ; - 1 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", 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["1", "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 262144 ( 696150 2 ( 20 z + 9 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 5 / 4 ( 1 - z ) 33 / 4 + 696150 2 ( 20 z + 9 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 5 / 4 ( 1 - z ) 33 / 4 - 348075 2 ( 20 z + 9 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 5 / 4 ( 1 - z ) 33 / 4 + 348075 2 ( 20 z + 9 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 5 / 4 ( 1 - z ) 33 / 4 + 8 ( 4608 z 6 - 46848 z 5 + 240720 z 4 - 1014960 z 3 - 7475455 z 2 - 1835008 z + 32768 ) ( z - 1 ) 8 ) HypergeometricPFQ 2 6 -1 1 4 z 1 262144 696150 2 1 2 20 z 9 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 z 5 4 1 -1 z 33 4 -1 696150 2 1 2 20 z 9 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 z 5 4 1 -1 z 33 4 -1 -1 348075 2 1 2 20 z 9 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 5 4 1 -1 z 33 4 -1 348075 2 1 2 20 z 9 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 5 4 1 -1 z 33 4 -1 8 4608 z 6 -1 46848 z 5 240720 z 4 -1 1014960 z 3 -1 7475455 z 2 -1 1835008 z 32768 z -1 8 -1 [/itex]

 Rule Form

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

 2007-05-02