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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.by91.01

 Input Form

 Hypergeometric2F1[1/8, 6, 17/8, z] == (1/83886080) (3 (-((256 (-17725 + 42625 z - 36363 z^2 + 10695 z^3))/ (-1 + z)^4) - (1/z^(1/8)) (2919735 (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)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(9/8)) (74865 (8 z^(1/8) + 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)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 6 ; 17 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["1", "8"], 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[FractionBox["17", "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 83886080 ( 3 ( - 256 ( 10695 z 3 - 36363 z 2 + 42625 z - 17725 ) ( z - 1 ) 4 - 1 z 8 ( 2919735 ( log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) - log ( z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) + ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) - 1 z 9 / 8 ( 74865 ( log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) - log ( z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) + ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 8 z 8 ) ) ) ) HypergeometricPFQ 1 8 6 17 8 z 1 83886080 3 -1 256 10695 z 3 -1 36363 z 2 42625 z -17725 z -1 4 -1 -1 1 z 1 8 -1 2919735 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -1 z 1 8 1 -1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 3 4 -1 1 4 z 1 8 1 -1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 1 4 -1 3 4 z 1 8 1 -1 1 z 9 8 -1 74865 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -1 z 1 8 1 -1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 3 4 -1 1 4 z 1 8 1 -1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 1 4 -1 3 4 z 1 8 1 8 z 1 8 [/itex]

 Rule Form

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

 2007-05-02