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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b0eb.01

 Input Form

 Hypergeometric2F1[8/5, 4, 23/5, z] == -((1/(15625 (-1 + z) z^(18/5))) (156 (-1)^(1/5) (-520 (-1)^(4/5) z^(3/5) + 165 (-1)^(4/5) z^(8/5) + 105 (-1)^(4/5) z^(13/5) + 6 (-1)^(4/5) (-52 + 36 z + 9 z^2 + 7 z^3) Log[1 - z^(1/5)] - 6 (-1)^(1/5) (-52 + 36 z + 9 z^2 + 7 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + 312 (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] - 216 (-1)^(3/5) z Log[1 - (-1)^(2/5) z^(1/5)] - 54 (-1)^(3/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] - 42 (-1)^(3/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 312 Log[1 + (-1)^(3/5) z^(1/5)] + 216 z Log[1 + (-1)^(3/5) z^(1/5)] + 54 z^2 Log[1 + (-1)^(3/5) z^(1/5)] + 42 z^3 Log[1 + (-1)^(3/5) z^(1/5)] - 312 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)] + 216 (-1)^(2/5) z Log[1 - (-1)^(4/5) z^(1/5)] + 54 (-1)^(2/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 42 (-1)^(2/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( 8 5 , 4 ; 23 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["8", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["23", "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 15625 ( z - 1 ) z 18 / 5 ( 156 - 1 5 ( - 42 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 + 42 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 + 42 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 105 ( - 1 ) 4 / 5 z 13 / 5 - 54 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 + 54 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 + 54 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 + 165 ( - 1 ) 4 / 5 z 8 / 5 - 216 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z + 216 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z + 216 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z - 520 ( - 1 ) 4 / 5 z 3 / 5 + 6 ( - 1 ) 4 / 5 ( 7 z 3 + 9 z 2 + 36 z - 52 ) log ( 1 - z 5 ) - 6 - 1 5 ( 7 z 3 + 9 z 2 + 36 z - 52 ) log ( - 1 5 z 5 + 1 ) + 312 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 312 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 312 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ 8 5 4 23 5 z -1 1 15625 z -1 z 18 5 -1 156 -1 1 5 -42 -1 3 5 1 -1 -1 2 5 z 1 5 z 3 42 -1 3 5 z 1 5 1 z 3 42 -1 2 5 1 -1 -1 4 5 z 1 5 z 3 105 -1 4 5 z 13 5 -1 54 -1 3 5 1 -1 -1 2 5 z 1 5 z 2 54 -1 3 5 z 1 5 1 z 2 54 -1 2 5 1 -1 -1 4 5 z 1 5 z 2 165 -1 4 5 z 8 5 -1 216 -1 3 5 1 -1 -1 2 5 z 1 5 z 216 -1 3 5 z 1 5 1 z 216 -1 2 5 1 -1 -1 4 5 z 1 5 z -1 520 -1 4 5 z 3 5 6 -1 4 5 7 z 3 9 z 2 36 z -52 1 -1 z 1 5 -1 6 -1 1 5 7 z 3 9 z 2 36 z -52 -1 1 5 z 1 5 1 312 -1 3 5 1 -1 -1 2 5 z 1 5 -1 312 -1 3 5 z 1 5 1 -1 312 -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