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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c1uy.01

 Input Form

 Hypergeometric2F1[1, 4, 27/8, z] == (1/(49152 (-1 + z) z^(19/8))) (19 (16 z^(3/8) (55 + 40 z - 128 z^2) - (330 (-1)^(1/8) (-1 + (-1)^(3/4)) ArcTan[1 - (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))])/(1 - z)^(5/8) - (330 (-1)^(1/8) (-1 + (-1)^(3/4)) ArcTan[1 + (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))])/(1 - z)^(5/8) + (330 (-1)^(3/8) (-1 + (-1)^(1/4)) ArcTan[1 - (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))])/(1 - z)^(5/8) + (330 (-1)^(3/8) (-1 + (-1)^(1/4)) ArcTan[1 + (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))])/(1 - z)^(5/8) - (165 (-1)^(3/8) (-1 + (-1)^(1/4)) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)])/(1 - z)^(5/8) + (165 (-1)^(3/8) (-1 + (-1)^(1/4)) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)])/(1 - z)^(5/8) + (165 (-1)^(1/8) (-1 + (-1)^(3/4)) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)])/(1 - z)^(5/8) - (165 (-1)^(1/8) (-1 + (-1)^(3/4)) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)])/(1 - z)^(5/8)))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 4 ; 27 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["27", "8"], 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 49152 ( z - 1 ) z 19 / 8 ( 19 ( 16 z 3 / 8 ( - 128 z 2 + 40 z + 55 ) - 330 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) tan - 1 ( 1 - z 8 cos ( π 8 ) 1 - z 8 , - z 8 sin ( π 8 ) 1 - z 8 ) ( 1 - z ) 5 / 8 - 330 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) tan - 1 ( cos ( π 8 ) z 8 1 - z 8 + 1 , - z 8 sin ( π 8 ) 1 - z 8 ) ( 1 - z ) 5 / 8 + 330 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) tan - 1 ( 1 - z 8 sin ( π 8 ) 1 - z 8 , - z 8 cos ( π 8 ) 1 - z 8 ) ( 1 - z ) 5 / 8 + 330 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) tan - 1 ( sin ( π 8 ) z 8 1 - z 8 + 1 , - z 8 cos ( π 8 ) 1 - z 8 ) ( 1 - z ) 5 / 8 - 165 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) log ( z 4 1 - z 4 - 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) ( 1 - z ) 5 / 8 + 165 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) log ( z 4 1 - z 4 + 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) ( 1 - z ) 5 / 8 + 165 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) log ( z 4 1 - z 4 - 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) ( 1 - z ) 5 / 8 - 165 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) log ( z 4 1 - z 4 + 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) ( 1 - z ) 5 / 8 ) ) HypergeometricPFQ 1 4 27 8 z 1 49152 z -1 z 19 8 -1 19 16 z 3 8 -128 z 2 40 z 55 -1 330 -1 1 8 -1 -1 3 4 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 1 -1 z 5 8 -1 -1 330 -1 1 8 -1 -1 3 4 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 1 -1 z 5 8 -1 330 -1 3 8 -1 -1 1 4 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 1 -1 z 5 8 -1 330 -1 3 8 -1 -1 1 4 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 1 -1 z 5 8 -1 -1 165 -1 3 8 -1 -1 1 4 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 1 -1 z 5 8 -1 165 -1 3 8 -1 -1 1 4 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 1 -1 z 5 8 -1 165 -1 1 8 -1 -1 3 4 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 1 -1 z 5 8 -1 -1 165 -1 1 8 -1 -1 3 4 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 1 -1 z 5 8 -1 [/itex]

 Rule Form

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

 2007-05-02