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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(4/5), 6, 21/5, z] == -((1/(48828125 (-1 + z) z^(16/5))) (88 (-1)^(1/5) (990 (-1)^(4/5) z^(1/5) + 4215 (-1)^(4/5) z^(6/5) + 19665 (-1)^(4/5) z^(11/5) - 192185 (-1)^(4/5) z^(16/5) + 173565 (-1)^(4/5) z^(21/5) + 18 (-1)^(4/5) (11 + 45 z + 210 z^2 + 3990 z^3 - 11970 z^4 + 7714 z^5) Log[1 - z^(1/5)] - 18 (-1)^(3/5) (11 + 45 z + 210 z^2 + 3990 z^3 - 11970 z^4 + 7714 z^5) Log[1 + (-1)^(1/5) z^(1/5)] + 198 (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] + 810 (-1)^(2/5) z Log[1 - (-1)^(2/5) z^(1/5)] + 3780 (-1)^(2/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 71820 (-1)^(2/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 215460 (-1)^(2/5) z^4 Log[1 - (-1)^(2/5) z^(1/5)] + 138852 (-1)^(2/5) z^5 Log[1 - (-1)^(2/5) z^(1/5)] - 198 (-1)^(1/5) Log[1 + (-1)^(3/5) z^(1/5)] - 810 (-1)^(1/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 3780 (-1)^(1/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 71820 (-1)^(1/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] + 215460 (-1)^(1/5) z^4 Log[1 + (-1)^(3/5) z^(1/5)] - 138852 (-1)^(1/5) z^5 Log[1 + (-1)^(3/5) z^(1/5)] + 198 Log[1 - (-1)^(4/5) z^(1/5)] + 810 z Log[1 - (-1)^(4/5) z^(1/5)] + 3780 z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 71820 z^3 Log[1 - (-1)^(4/5) z^(1/5)] - 215460 z^4 Log[1 - (-1)^(4/5) z^(1/5)] + 138852 z^5 Log[1 - (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 4 5 , 6 ; 21 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["4", "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["21", "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 48828125 ( z - 1 ) z 16 / 5 ( 88 - 1 5 ( 138852 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 5 - 138852 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 5 + 138852 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 5 + 173565 ( - 1 ) 4 / 5 z 21 / 5 - 215460 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 4 + 215460 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 4 - 215460 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 4 - 192185 ( - 1 ) 4 / 5 z 16 / 5 + 71820 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 - 71820 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 + 71820 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 19665 ( - 1 ) 4 / 5 z 11 / 5 + 3780 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 - 3780 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 + 3780 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 + 4215 ( - 1 ) 4 / 5 z 6 / 5 + 810 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z - 810 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z + 810 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z + 990 ( - 1 ) 4 / 5 z 5 + 18 ( - 1 ) 4 / 5 ( 7714 z 5 - 11970 z 4 + 3990 z 3 + 210 z 2 + 45 z + 11 ) log ( 1 - z 5 ) - 18 ( - 1 ) 3 / 5 ( 7714 z 5 - 11970 z 4 + 3990 z 3 + 210 z 2 + 45 z + 11 ) log ( - 1 5 z 5 + 1 ) + 198 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 198 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 198 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ -1 4 5 6 21 5 z -1 1 48828125 z -1 z 16 5 -1 88 -1 1 5 138852 -1 2 5 1 -1 -1 2 5 z 1 5 z 5 -1 138852 -1 1 5 -1 3 5 z 1 5 1 z 5 138852 1 -1 -1 4 5 z 1 5 z 5 173565 -1 4 5 z 21 5 -1 215460 -1 2 5 1 -1 -1 2 5 z 1 5 z 4 215460 -1 1 5 -1 3 5 z 1 5 1 z 4 -1 215460 1 -1 -1 4 5 z 1 5 z 4 -1 192185 -1 4 5 z 16 5 71820 -1 2 5 1 -1 -1 2 5 z 1 5 z 3 -1 71820 -1 1 5 -1 3 5 z 1 5 1 z 3 71820 1 -1 -1 4 5 z 1 5 z 3 19665 -1 4 5 z 11 5 3780 -1 2 5 1 -1 -1 2 5 z 1 5 z 2 -1 3780 -1 1 5 -1 3 5 z 1 5 1 z 2 3780 1 -1 -1 4 5 z 1 5 z 2 4215 -1 4 5 z 6 5 810 -1 2 5 1 -1 -1 2 5 z 1 5 z -1 810 -1 1 5 -1 3 5 z 1 5 1 z 810 1 -1 -1 4 5 z 1 5 z 990 -1 4 5 z 1 5 18 -1 4 5 7714 z 5 -1 11970 z 4 3990 z 3 210 z 2 45 z 11 1 -1 z 1 5 -1 18 -1 3 5 7714 z 5 -1 11970 z 4 3990 z 3 210 z 2 45 z 11 -1 1 5 z 1 5 1 198 -1 2 5 1 -1 -1 2 5 z 1 5 -1 198 -1 1 5 -1 3 5 z 1 5 1 198 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