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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b1rk.01

 Input Form

 Hypergeometric2F1[12/5, 5, 27/5, -z] == (1/(78125 z^(22/5) (1 + z)^2)) (187 (-1)^(1/5) (3570 (-1)^(4/5) z^(2/5) + 4860 (-1)^(4/5) z^(7/5) + 385 (-1)^(4/5) z^(12/5) - 280 (-1)^(4/5) z^(17/5) + 84 (-1)^(4/5) (1 + z)^2 (17 - 6 z + 2 z^2) Log[1 + z^(1/5)] + 84 (-1)^(2/5) (1 + z)^2 (17 - 6 z + 2 z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 1428 Log[1 + (-1)^(2/5) z^(1/5)] + 2352 z Log[1 + (-1)^(2/5) z^(1/5)] + 588 z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 168 z^3 Log[1 + (-1)^(2/5) z^(1/5)] + 168 z^4 Log[1 + (-1)^(2/5) z^(1/5)] - 1428 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] - 2352 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] - 588 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 168 (-1)^(3/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 168 (-1)^(3/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] - 1428 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 2352 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 588 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] + 168 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 168 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( 12 5 , 5 ; 27 5 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["12", "5"], 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["27", "5"], 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 78125 z 22 / 5 ( z + 1 ) 2 ( 187 - 1 5 ( 168 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 - 168 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 168 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 - 280 ( - 1 ) 4 / 5 z 17 / 5 - 168 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 + 168 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 + 168 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 + 385 ( - 1 ) 4 / 5 z 12 / 5 + 588 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 - 588 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 - 588 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 4860 ( - 1 ) 4 / 5 z 7 / 5 + 2352 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 2352 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 2352 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 3570 ( - 1 ) 4 / 5 z 2 / 5 + 84 ( - 1 ) 4 / 5 ( z + 1 ) 2 ( 2 z 2 - 6 z + 17 ) log ( z 5 + 1 ) + 84 ( - 1 ) 2 / 5 ( z + 1 ) 2 ( 2 z 2 - 6 z + 17 ) log ( 1 - - 1 5 z 5 ) + 1428 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 1428 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 1428 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ 12 5 5 27 5 -1 z 1 78125 z 22 5 z 1 2 -1 187 -1 1 5 168 -1 2 5 z 1 5 1 z 4 -1 168 -1 3 5 1 -1 -1 3 5 z 1 5 z 4 -1 168 -1 1 5 -1 4 5 z 1 5 1 z 4 -1 280 -1 4 5 z 17 5 -1 168 -1 2 5 z 1 5 1 z 3 168 -1 3 5 1 -1 -1 3 5 z 1 5 z 3 168 -1 1 5 -1 4 5 z 1 5 1 z 3 385 -1 4 5 z 12 5 588 -1 2 5 z 1 5 1 z 2 -1 588 -1 3 5 1 -1 -1 3 5 z 1 5 z 2 -1 588 -1 1 5 -1 4 5 z 1 5 1 z 2 4860 -1 4 5 z 7 5 2352 -1 2 5 z 1 5 1 z -1 2352 -1 3 5 1 -1 -1 3 5 z 1 5 z -1 2352 -1 1 5 -1 4 5 z 1 5 1 z 3570 -1 4 5 z 2 5 84 -1 4 5 z 1 2 2 z 2 -1 6 z 17 z 1 5 1 84 -1 2 5 z 1 2 2 z 2 -1 6 z 17 1 -1 -1 1 5 z 1 5 1428 -1 2 5 z 1 5 1 -1 1428 -1 3 5 1 -1 -1 3 5 z 1 5 -1 1428 -1 1 5 -1 4 5 z 1 5 1 [/itex]

 Rule Form

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

 2007-05-02