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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.cd8k.01

 Input Form

 Hypergeometric2F1[39/8, 5, 47/8, -z] == (1/262144) (13 (-((8 (-601 + 6461 z + 6405 z^2 + 2415 z^3))/(1 + z)^4) + (1/z^(39/8)) (-85560 z^(7/8) + 39928 z^(15/8) - 26040 z^(23/8) + 19320 z^(31/8) + 74865 (-1)^(1/8) Log[1 - (-1)^(1/8) z^(1/8)] - 74865 (-1)^(1/8) Log[1 + (-1)^(1/8) z^(1/8)] + 74865 (-1)^(3/8) Log[1 - (-1)^(3/8) z^(1/8)] - 74865 (-1)^(3/8) Log[1 + (-1)^(3/8) z^(1/8)] + 74865 (-1)^(5/8) Log[1 - (-1)^(5/8) z^(1/8)] - 74865 (-1)^(5/8) Log[1 + (-1)^(5/8) z^(1/8)] + 74865 (-1)^(7/8) Log[1 - (-1)^(7/8) z^(1/8)] - 74865 (-1)^(7/8) Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 39 8 , 5 ; 47 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["39", "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["47", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 ( 13 ( 1 z 39 / 8 ( 19320 z 31 / 8 - 26040 z 23 / 8 + 39928 z 15 / 8 - 85560 z 7 / 8 + 74865 - 1 8 log ( 1 - - 1 8 z 8 ) - 74865 - 1 8 log ( - 1 8 z 8 + 1 ) + 74865 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 74865 ( - 1 ) 3 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 74865 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 74865 ( - 1 ) 5 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 74865 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 74865 ( - 1 ) 7 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) - 8 ( 2415 z 3 + 6405 z 2 + 6461 z - 601 ) ( z + 1 ) 4 ) ) HypergeometricPFQ 39 8 5 47 8 -1 z 1 262144 13 1 z 39 8 -1 19320 z 31 8 -1 26040 z 23 8 39928 z 15 8 -1 85560 z 7 8 74865 -1 1 8 1 -1 -1 1 8 z 1 8 -1 74865 -1 1 8 -1 1 8 z 1 8 1 74865 -1 3 8 1 -1 -1 3 8 z 1 8 -1 74865 -1 3 8 -1 3 8 z 1 8 1 74865 -1 5 8 1 -1 -1 5 8 z 1 8 -1 74865 -1 5 8 -1 5 8 z 1 8 1 74865 -1 7 8 1 -1 -1 7 8 z 1 8 -1 74865 -1 7 8 -1 7 8 z 1 8 1 -1 8 2415 z 3 6405 z 2 6461 z -601 z 1 4 -1 [/itex]

 Rule Form

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

 2007-05-02