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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c1n7.01

 Input Form

 Hypergeometric2F1[1, 2, 13/8, z] == (1/(128 (1 - z)^(11/8) z^(5/8))) (5 (16 (1 - z)^(3/8) z^(5/8) + 6 (-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))] + 6 (-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))] - 3 (-1)^(3/8) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Cos[Pi/8])/ (1 - z)^(1/8)] + 3 (-1)^(5/8) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)] - 3 (-1)^(1/8) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Sin[Pi/8])/ (1 - z)^(1/8)] + 3 (-1)^(7/8) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)] + 6 Cos[Pi/8] Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Sin[Pi/8])/ (1 - z)^(1/8)] + 12 ArcTan[1 - (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))] Sin[Pi/8] + 12 ArcTan[1 + (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))] Sin[Pi/8] + 6 Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)] Sin[Pi/8]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 2 ; 13 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["13", "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] 1 128 ( 1 - z ) 11 / 8 z 5 / 8 ( 5 ( 6 - 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 ) + 6 - 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 ) + 3 ( - 1 ) 5 / 8 log ( z 4 1 - z 4 + 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) - 3 ( - 1 ) 3 / 8 log ( z 4 1 - z 4 + 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) + 3 ( - 1 ) 7 / 8 log ( z 4 1 - z 4 - 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) - 3 - 1 8 log ( z 4 1 - z 4 - 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) + 6 cos ( π 8 ) log ( z 4 1 - z 4 + 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) + 16 ( 1 - z ) 3 / 8 z 5 / 8 + 12 tan - 1 ( 1 - z 8 sin ( π 8 ) 1 - z 8 , - z 8 cos ( π 8 ) 1 - z 8 ) sin ( π 8 ) + 12 tan - 1 ( sin ( π 8 ) z 8 1 - z 8 + 1 , - z 8 cos ( π 8 ) 1 - z 8 ) sin ( π 8 ) + 6 log ( z 4 1 - z 4 - 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) sin ( π 8 ) ) ) HypergeometricPFQ 1 2 13 8 z 1 128 1 -1 z 11 8 z 5 8 -1 5 6 -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 6 -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 3 -1 5 8 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 3 -1 3 8 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 3 -1 7 8 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 3 -1 1 8 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 6 8 -1 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 16 1 -1 z 3 8 z 5 8 12 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 8 -1 12 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 8 -1 6 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 8 -1 [/itex]

 Rule Form

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

 2007-05-02