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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c3xy.01

 Input Form

 Hypergeometric2F1[11/8, 6, 27/8, -z] == (1/83886080) (209 ((256 (1705 + 2905 z + 1911 z^2 + 455 z^3))/(1 + z)^4 - (1/z^(19/8)) (455 (-88 z^(3/8) + 24 z^(11/8) + 33 (-1)^(5/8) Log[1 - (-1)^(1/8) z^(1/8)] - 33 (-1)^(5/8) Log[1 + (-1)^(1/8) z^(1/8)] - 33 (-1)^(7/8) Log[1 - (-1)^(3/8) z^(1/8)] + 33 (-1)^(7/8) Log[1 + (-1)^(3/8) z^(1/8)] - 33 (-1)^(1/8) Log[1 - (-1)^(5/8) z^(1/8)] + 33 (-1)^(1/8) Log[1 + (-1)^(5/8) z^(1/8)] + 33 (-1)^(3/8) Log[1 - (-1)^(7/8) z^(1/8)] - 33 (-1)^(3/8) Log[1 + (-1)^(7/8) z^(1/8)])) - (1/z^(11/8)) (13195 (8 z^(3/8) - 3 (-1)^(5/8) Log[1 - (-1)^(1/8) z^(1/8)] + 3 (-1)^(5/8) Log[1 + (-1)^(1/8) z^(1/8)] + 3 (-1)^(7/8) Log[1 - (-1)^(3/8) z^(1/8)] - 3 (-1)^(7/8) Log[1 + (-1)^(3/8) z^(1/8)] + 3 (-1)^(1/8) Log[1 - (-1)^(5/8) z^(1/8)] - 3 (-1)^(1/8) Log[1 + (-1)^(5/8) z^(1/8)] - 3 (-1)^(3/8) Log[1 - (-1)^(7/8) z^(1/8)] + 3 (-1)^(3/8) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 11 8 , 6 ; 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[FractionBox["11", "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["27", "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 83886080 ( 209 ( 256 ( 455 z 3 + 1911 z 2 + 2905 z + 1705 ) ( z + 1 ) 4 - 1 z 19 / 8 ( 455 ( 24 z 11 / 8 - 88 z 3 / 8 + 33 ( - 1 ) 5 / 8 log ( 1 - - 1 8 z 8 ) - 33 ( - 1 ) 5 / 8 log ( - 1 8 z 8 + 1 ) - 33 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 33 ( - 1 ) 7 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 33 - 1 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 33 - 1 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 33 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 33 ( - 1 ) 3 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) - 1 z 11 / 8 ( 13195 ( - 3 ( - 1 ) 5 / 8 log ( 1 - - 1 8 z 8 ) + 3 ( - 1 ) 5 / 8 log ( - 1 8 z 8 + 1 ) + 3 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 3 ( - 1 ) 7 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 3 - 1 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 3 - 1 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 3 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 3 ( - 1 ) 3 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) + 8 z 3 / 8 ) ) ) ) HypergeometricPFQ 11 8 6 27 8 -1 z 1 83886080 209 256 455 z 3 1911 z 2 2905 z 1705 z 1 4 -1 -1 1 z 19 8 -1 455 24 z 11 8 -1 88 z 3 8 33 -1 5 8 1 -1 -1 1 8 z 1 8 -1 33 -1 5 8 -1 1 8 z 1 8 1 -1 33 -1 7 8 1 -1 -1 3 8 z 1 8 33 -1 7 8 -1 3 8 z 1 8 1 -1 33 -1 1 8 1 -1 -1 5 8 z 1 8 33 -1 1 8 -1 5 8 z 1 8 1 33 -1 3 8 1 -1 -1 7 8 z 1 8 -1 33 -1 3 8 -1 7 8 z 1 8 1 -1 1 z 11 8 -1 13195 -3 -1 5 8 1 -1 -1 1 8 z 1 8 3 -1 5 8 -1 1 8 z 1 8 1 3 -1 7 8 1 -1 -1 3 8 z 1 8 -1 3 -1 7 8 -1 3 8 z 1 8 1 3 -1 1 8 1 -1 -1 5 8 z 1 8 -1 3 -1 1 8 -1 5 8 z 1 8 1 -1 3 -1 3 8 1 -1 -1 7 8 z 1 8 3 -1 3 8 -1 7 8 z 1 8 1 8 z 3 8 [/itex]

 Rule Form

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

 2007-05-02