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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b08d.01

 Input Form

 Hypergeometric2F1[7/5, 6, 22/5, z] == (1/1953125) (119 (-((125 (157 - 204 z + 72 z^2))/(-1 + z)^3) + (1/z^(7/5)) (1404 (5 z^(2/5) + 2 Log[1 - z^(1/5)] - 2 (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - 2 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + 2 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 2 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)])) + (1/z^(12/5)) (156 (35 z^(2/5) + 10 z^(7/5) + 14 Log[1 - z^(1/5)] - 14 (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - 14 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + 14 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 14 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)])) + (1/z^(17/5)) (12 (210 z^(2/5) + 60 z^(7/5) + 35 z^(12/5) + 84 Log[1 - z^(1/5)] - 84 (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - 84 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + 84 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 84 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 7 5 , 6 ; 22 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["7", "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[FractionBox["22", "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 ( 119 ( - 125 ( 72 z 2 - 204 z + 157 ) ( z - 1 ) 3 + 1 z 7 / 5 ( 1404 ( 2 log ( 1 - z 5 ) - 2 ( - 1 ) 3 / 5 log ( - 1 5 z 5 + 1 ) - 2 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 2 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 2 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) + 5 z 2 / 5 ) ) + 1 z 12 / 5 ( 156 ( 10 z 7 / 5 + 35 z 2 / 5 + 14 log ( 1 - z 5 ) - 14 ( - 1 ) 3 / 5 log ( - 1 5 z 5 + 1 ) - 14 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 14 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 14 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) + 1 z 17 / 5 ( 12 ( 35 z 12 / 5 + 60 z 7 / 5 + 210 z 2 / 5 + 84 log ( 1 - z 5 ) - 84 ( - 1 ) 3 / 5 log ( - 1 5 z 5 + 1 ) - 84 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 84 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 84 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) ) ) HypergeometricPFQ 7 5 6 22 5 z 1 1953125 119 -1 125 72 z 2 -1 204 z 157 z -1 3 -1 1 z 7 5 -1 1404 2 1 -1 z 1 5 -1 2 -1 3 5 -1 1 5 z 1 5 1 -1 2 -1 1 5 1 -1 -1 2 5 z 1 5 2 -1 4 5 -1 3 5 z 1 5 1 2 -1 2 5 1 -1 -1 4 5 z 1 5 5 z 2 5 1 z 12 5 -1 156 10 z 7 5 35 z 2 5 14 1 -1 z 1 5 -1 14 -1 3 5 -1 1 5 z 1 5 1 -1 14 -1 1 5 1 -1 -1 2 5 z 1 5 14 -1 4 5 -1 3 5 z 1 5 1 14 -1 2 5 1 -1 -1 4 5 z 1 5 1 z 17 5 -1 12 35 z 12 5 60 z 7 5 210 z 2 5 84 1 -1 z 1 5 -1 84 -1 3 5 -1 1 5 z 1 5 1 -1 84 -1 1 5 1 -1 -1 2 5 z 1 5 84 -1 4 5 -1 3 5 z 1 5 1 84 -1 2 5 1 -1 -1 4 5 z 1 5 [/itex]

 Rule Form

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

 2007-05-02