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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c3rt.01

 Input Form

 Hypergeometric2F1[11/8, 5, 43/8, z] == -((65835 (-1)^(1/4) (-15048 (-1)^(3/4) z^(3/8) + 2584 (-1)^(3/4) z^(11/8) + 2088 (-1)^(3/4) z^(19/8) + 2184 (-1)^(3/4) z^(27/8) + 3 (-1)^(3/4) (-1881 + 836 z + 330 z^2 + 260 z^3 + 455 z^4) Log[1 - z^(1/8)] - 3 (-1)^(1/4) (-1881 + 836 z + 330 z^2 + 260 z^3 + 455 z^4) Log[1 - I z^(1/8)] - 5643 (-1)^(1/4) Log[1 + I z^(1/8)] + 2508 (-1)^(1/4) z Log[1 + I z^(1/8)] + 990 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] + 780 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] + 1365 (-1)^(1/4) z^4 Log[1 + I z^(1/8)] + 5643 (-1)^(3/4) Log[1 + z^(1/8)] - 2508 (-1)^(3/4) z Log[1 + z^(1/8)] - 990 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 780 (-1)^(3/4) z^3 Log[1 + z^(1/8)] - 1365 (-1)^(3/4) z^4 Log[1 + z^(1/8)] - 5643 Log[1 - (-1)^(1/4) z^(1/8)] + 2508 z Log[1 - (-1)^(1/4) z^(1/8)] + 990 z^2 Log[1 - (-1)^(1/4) z^(1/8)] + 780 z^3 Log[1 - (-1)^(1/4) z^(1/8)] + 1365 z^4 Log[1 - (-1)^(1/4) z^(1/8)] + 5643 Log[1 + (-1)^(1/4) z^(1/8)] - 2508 z Log[1 + (-1)^(1/4) z^(1/8)] - 990 z^2 Log[1 + (-1)^(1/4) z^(1/8)] - 780 z^3 Log[1 + (-1)^(1/4) z^(1/8)] - 1365 z^4 Log[1 + (-1)^(1/4) z^(1/8)] - 5643 I Log[1 - (-1)^(3/4) z^(1/8)] + 2508 I z Log[1 - (-1)^(3/4) z^(1/8)] + 990 I z^2 Log[1 - (-1)^(3/4) z^(1/8)] + 780 I z^3 Log[1 - (-1)^(3/4) z^(1/8)] + 1365 I z^4 Log[1 - (-1)^(3/4) z^(1/8)] + 5643 I Log[1 + (-1)^(3/4) z^(1/8)] - 2508 I z Log[1 + (-1)^(3/4) z^(1/8)] - 990 I z^2 Log[1 + (-1)^(3/4) z^(1/8)] - 780 I z^3 Log[1 + (-1)^(3/4) z^(1/8)] - 1365 I z^4 Log[1 + (-1)^(3/4) z^(1/8)]))/(268435456 (-1 + z) z^(35/8)))

 Standard Form

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 MathML Form

 2 F 1 ( 11 8 , 5 ; 43 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["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["43", "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 268435456 ( z - 1 ) z 35 / 8 ( 65835 - 1 4 ( 1365 - 1 4 log ( z 8 + 1 ) z 4 - 1365 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 4 + 1365 log ( 1 - - 1 4 z 8 ) z 4 - 1365 log ( - 1 4 z 8 + 1 ) z 4 + 1365 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 4 - 1365 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 4 + 2184 ( - 1 ) 3 / 4 z 27 / 8 + 780 - 1 4 log ( z 8 + 1 ) z 3 - 780 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 3 + 780 log ( 1 - - 1 4 z 8 ) z 3 - 780 log ( - 1 4 z 8 + 1 ) z 3 + 780 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 3 - 780 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 3 + 2088 ( - 1 ) 3 / 4 z 19 / 8 + 990 - 1 4 log ( z 8 + 1 ) z 2 - 990 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 2 + 990 log ( 1 - - 1 4 z 8 ) z 2 - 990 log ( - 1 4 z 8 + 1 ) z 2 + 990 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 2 - 990 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 2 + 2584 ( - 1 ) 3 / 4 z 11 / 8 + 2508 - 1 4 log ( z 8 + 1 ) z - 2508 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z + 2508 log ( 1 - - 1 4 z 8 ) z - 2508 log ( - 1 4 z 8 + 1 ) z + 2508 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z - 2508 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z - 15048 ( - 1 ) 3 / 4 z 3 / 8 + 3 ( - 1 ) 3 / 4 ( 455 z 4 + 260 z 3 + 330 z 2 + 836 z - 1881 ) log ( 1 - z 8 ) - 3 - 1 4 ( 455 z 4 + 260 z 3 + 330 z 2 + 836 z - 1881 ) log ( 1 - z 8 ) - 5643 - 1 4 log ( z 8 + 1 ) + 5643 ( - 1 ) 3 / 4 log ( z 8 + 1 ) - 5643 log ( 1 - - 1 4 z 8 ) + 5643 log ( - 1 4 z 8 + 1 ) - 5643 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 5643 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) HypergeometricPFQ 11 8 5 43 8 z -1 1 268435456 z -1 z 35 8 -1 65835 -1 1 4 1365 -1 1 4 z 1 8 1 z 4 -1 1365 -1 3 4 z 1 8 1 z 4 1365 1 -1 -1 1 4 z 1 8 z 4 -1 1365 -1 1 4 z 1 8 1 z 4 1365 1 -1 -1 3 4 z 1 8 z 4 -1 1365 -1 3 4 z 1 8 1 z 4 2184 -1 3 4 z 27 8 780 -1 1 4 z 1 8 1 z 3 -1 780 -1 3 4 z 1 8 1 z 3 780 1 -1 -1 1 4 z 1 8 z 3 -1 780 -1 1 4 z 1 8 1 z 3 780 1 -1 -1 3 4 z 1 8 z 3 -1 780 -1 3 4 z 1 8 1 z 3 2088 -1 3 4 z 19 8 990 -1 1 4 z 1 8 1 z 2 -1 990 -1 3 4 z 1 8 1 z 2 990 1 -1 -1 1 4 z 1 8 z 2 -1 990 -1 1 4 z 1 8 1 z 2 990 1 -1 -1 3 4 z 1 8 z 2 -1 990 -1 3 4 z 1 8 1 z 2 2584 -1 3 4 z 11 8 2508 -1 1 4 z 1 8 1 z -1 2508 -1 3 4 z 1 8 1 z 2508 1 -1 -1 1 4 z 1 8 z -1 2508 -1 1 4 z 1 8 1 z 2508 1 -1 -1 3 4 z 1 8 z -1 2508 -1 3 4 z 1 8 1 z -1 15048 -1 3 4 z 3 8 3 -1 3 4 455 z 4 260 z 3 330 z 2 836 z -1881 1 -1 z 1 8 -1 3 -1 1 4 455 z 4 260 z 3 330 z 2 836 z -1881 1 -1 z 1 8 -1 5643 -1 1 4 z 1 8 1 5643 -1 3 4 z 1 8 1 -1 5643 1 -1 -1 1 4 z 1 8 5643 -1 1 4 z 1 8 1 -1 5643 1 -1 -1 3 4 z 1 8 5643 -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