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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b0ty.01

 Input Form

 Hypergeometric2F1[9/5, 6, 19/5, z] == (1/781250) (21 (-((25 (-1552 + 1936 z - 891 z^2 + 132 z^3))/(-1 + z)^4) + (1/z^(9/5)) (528 (5 z^(4/5) + 4 Log[1 - z^(1/5)] - 4 (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + 4 (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - 4 (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + 4 (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)])) + (1/z^(14/5)) (33 (45 z^(4/5) + 20 z^(9/5) + 36 Log[1 - z^(1/5)] - 36 (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + 36 (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - 36 (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + 36 (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 9 5 , 6 ; 19 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["9", "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["19", "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 781250 ( 21 ( - 25 ( 132 z 3 - 891 z 2 + 1936 z - 1552 ) ( z - 1 ) 4 + 1 z 9 / 5 ( 528 ( 4 log ( 1 - z 5 ) - 4 - 1 5 log ( - 1 5 z 5 + 1 ) + 4 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 4 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 4 ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) + 5 z 4 / 5 ) ) + 1 z 14 / 5 ( 33 ( 20 z 9 / 5 + 45 z 4 / 5 + 36 log ( 1 - z 5 ) - 36 - 1 5 log ( - 1 5 z 5 + 1 ) + 36 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 36 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 36 ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) ) ) HypergeometricPFQ 9 5 6 19 5 z 1 781250 21 -1 25 132 z 3 -1 891 z 2 1936 z -1552 z -1 4 -1 1 z 9 5 -1 528 4 1 -1 z 1 5 -1 4 -1 1 5 -1 1 5 z 1 5 1 4 -1 2 5 1 -1 -1 2 5 z 1 5 -1 4 -1 3 5 -1 3 5 z 1 5 1 4 -1 4 5 1 -1 -1 4 5 z 1 5 5 z 4 5 1 z 14 5 -1 33 20 z 9 5 45 z 4 5 36 1 -1 z 1 5 -1 36 -1 1 5 -1 1 5 z 1 5 1 36 -1 2 5 1 -1 -1 2 5 z 1 5 -1 36 -1 3 5 -1 3 5 z 1 5 1 36 -1 4 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