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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(24/5), 6, -(9/5), z] == (1/1953125) (266 ((125 (8591 - 16497 z + 7956 z^2))/(-1 + z)^3 - 8767512 ((-(5/252)) (18 + 28 z + 63 z^2) - z^(14/5) (Log[1 - z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)])) + 40607424 (-(5/19) - (5 z)/14 - (5 z^2)/9 - (5 z^3)/4 - z^(19/5) (Log[1 - z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)])) - 41453412 (-(5/24) - (5 z)/19 - (5 z^2)/14 - (5 z^3)/9 - (5 z^4)/4 - z^(24/5) (Log[1 - z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 24 5 , 6 ; - 9 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["24", "5"]]], 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[RowBox[List["-", FractionBox["9", "5"]]], 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 1953125 ( 266 ( 125 ( 7956 z 2 - 16497 z + 8591 ) ( z - 1 ) 3 - 8767512 ( - ( log ( 1 - z 5 ) + ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 14 / 5 - 5 252 ( 63 z 2 + 28 z + 18 ) ) + 40607424 ( - ( log ( 1 - z 5 ) + ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 19 / 5 - 5 z 3 4 - 5 z 2 9 - 5 z 14 - 5 19 ) - 41453412 ( - ( log ( 1 - z 5 ) + ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 24 / 5 - 5 z 4 4 - 5 z 3 9 - 5 z 2 14 - 5 z 19 - 5 24 ) ) ) HypergeometricPFQ -1 24 5 6 -1 9 5 z 1 1953125 266 125 7956 z 2 -1 16497 z 8591 z -1 3 -1 -1 8767512 -1 1 -1 z 1 5 -1 4 5 -1 1 5 z 1 5 1 -1 -1 3 5 1 -1 -1 2 5 z 1 5 -1 2 5 -1 3 5 z 1 5 1 -1 -1 1 5 1 -1 -1 4 5 z 1 5 z 14 5 -1 5 252 63 z 2 28 z 18 40607424 -1 1 -1 z 1 5 -1 4 5 -1 1 5 z 1 5 1 -1 -1 3 5 1 -1 -1 2 5 z 1 5 -1 2 5 -1 3 5 z 1 5 1 -1 -1 1 5 1 -1 -1 4 5 z 1 5 z 19 5 -1 5 z 3 4 -1 -1 5 z 2 9 -1 -1 5 z 14 -1 -1 5 19 -1 41453412 -1 1 -1 z 1 5 -1 4 5 -1 1 5 z 1 5 1 -1 -1 3 5 1 -1 -1 2 5 z 1 5 -1 2 5 -1 3 5 z 1 5 1 -1 -1 1 5 1 -1 -1 4 5 z 1 5 z 24 5 -1 5 z 4 4 -1 -1 5 z 3 9 -1 -1 5 z 2 14 -1 -1 5 z 19 -1 -1 5 24 [/itex]

 Rule Form

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

 2007-05-02