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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c1cv.01

 Input Form

 Hypergeometric2F1[7/8, 5, 31/8, z] == (1/33554432) (805 (-((1024 (-35 + 27 z))/(-1 + z)^2) - (1/z^(23/8)) (9 (120 z^(7/8) + 56 z^(15/8) + 105 Log[1 - z^(1/8)] + 105 I Log[1 - I z^(1/8)] - 105 I Log[1 + I z^(1/8)] - 105 Log[1 + z^(1/8)] + 105 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - 105 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + 105 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - 105 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(15/8)) (306 (8 z^(7/8) + 7 Log[1 - z^(1/8)] + 7 I Log[1 - I z^(1/8)] - 7 I Log[1 + I z^(1/8)] - 7 Log[1 + z^(1/8)] + 7 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - 7 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + 7 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - 7 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(7/8)) (3825 (Log[1 - z^(1/8)] + I Log[1 - I z^(1/8)] - I Log[1 + I z^(1/8)] - Log[1 + z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 7 8 , 5 ; 31 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["31", "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 33554432 ( 805 ( - 1024 ( 27 z - 35 ) ( z - 1 ) 2 - 1 z 23 / 8 ( 9 ( 56 z 15 / 8 + 120 z 7 / 8 + 105 log ( 1 - z 8 ) + 105 log ( 1 - z 8 ) - 105 log ( z 8 + 1 ) - 105 log ( z 8 + 1 ) + 105 - 1 4 log ( 1 - - 1 4 z 8 ) - 105 - 1 4 log ( - 1 4 z 8 + 1 ) + 105 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 105 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) - 1 z 15 / 8 ( 306 ( 7 log ( 1 - z 8 ) + 7 log ( 1 - z 8 ) - 7 log ( z 8 + 1 ) - 7 log ( z 8 + 1 ) + 7 - 1 4 log ( 1 - - 1 4 z 8 ) - 7 - 1 4 log ( - 1 4 z 8 + 1 ) + 7 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 7 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 8 z 7 / 8 ) ) - 1 z 7 / 8 ( 3825 ( log ( 1 - z 8 ) + log ( 1 - z 8 ) - log ( z 8 + 1 ) - log ( z 8 + 1 ) + - 1 4 log ( 1 - - 1 4 z 8 ) - - 1 4 log ( - 1 4 z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) ) ) HypergeometricPFQ 7 8 5 31 8 z 1 33554432 805 -1 1024 27 z -35 z -1 2 -1 -1 1 z 23 8 -1 9 56 z 15 8 120 z 7 8 105 1 -1 z 1 8 105 1 -1 z 1 8 -1 105 z 1 8 1 -1 105 z 1 8 1 105 -1 1 4 1 -1 -1 1 4 z 1 8 -1 105 -1 1 4 -1 1 4 z 1 8 1 105 -1 3 4 1 -1 -1 3 4 z 1 8 -1 105 -1 3 4 -1 3 4 z 1 8 1 -1 1 z 15 8 -1 306 7 1 -1 z 1 8 7 1 -1 z 1 8 -1 7 z 1 8 1 -1 7 z 1 8 1 7 -1 1 4 1 -1 -1 1 4 z 1 8 -1 7 -1 1 4 -1 1 4 z 1 8 1 7 -1 3 4 1 -1 -1 3 4 z 1 8 -1 7 -1 3 4 -1 3 4 z 1 8 1 8 z 7 8 -1 1 z 7 8 -1 3825 1 -1 z 1 8 1 -1 z 1 8 -1 z 1 8 1 -1 z 1 8 1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 -1 1 4 -1 1 4 z 1 8 1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 -1 3 4 -1 3 4 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02