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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b08g.01

 Input Form

 Hypergeometric2F1[7/5, 6, 27/5, z] == -((1/(9765625 (-1 + z)^2 z^(22/5))) (1309 (-1)^(1/5) (3570 (-1)^(4/5) z^(2/5) - 1080 (-1)^(4/5) z^(7/5) - 1055 (-1)^(4/5) z^(12/5) - 1430 (-1)^(4/5) z^(17/5) + 3120 (-1)^(4/5) z^(22/5) + 12 (-1)^(4/5) (-1 + z)^2 (119 + 168 z + 182 z^2 + 156 z^3) Log[1 - z^(1/5)] + 12 (-1)^(2/5) (-1 + z)^2 (119 + 168 z + 182 z^2 + 156 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + 1428 Log[1 - (-1)^(2/5) z^(1/5)] - 840 z Log[1 - (-1)^(2/5) z^(1/5)] - 420 z^2 Log[1 - (-1)^(2/5) z^(1/5)] - 480 z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 1560 z^4 Log[1 - (-1)^(2/5) z^(1/5)] + 1872 z^5 Log[1 - (-1)^(2/5) z^(1/5)] - 1428 (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + 840 (-1)^(3/5) z Log[1 + (-1)^(3/5) z^(1/5)] + 420 (-1)^(3/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] + 480 (-1)^(3/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] + 1560 (-1)^(3/5) z^4 Log[1 + (-1)^(3/5) z^(1/5)] - 1872 (-1)^(3/5) z^5 Log[1 + (-1)^(3/5) z^(1/5)] - 1428 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)] + 840 (-1)^(1/5) z Log[1 - (-1)^(4/5) z^(1/5)] + 420 (-1)^(1/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 480 (-1)^(1/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)] + 1560 (-1)^(1/5) z^4 Log[1 - (-1)^(4/5) z^(1/5)] - 1872 (-1)^(1/5) z^5 Log[1 - (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( 7 5 , 6 ; 27 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["27", "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 9765625 ( z - 1 ) 2 z 22 / 5 ( 1309 - 1 5 ( 1872 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 5 - 1872 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 5 - 1872 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 5 + 3120 ( - 1 ) 4 / 5 z 22 / 5 - 1560 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 4 + 1560 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 4 + 1560 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 4 - 1430 ( - 1 ) 4 / 5 z 17 / 5 - 480 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 + 480 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 + 480 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 - 1055 ( - 1 ) 4 / 5 z 12 / 5 - 420 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 + 420 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 + 420 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 - 1080 ( - 1 ) 4 / 5 z 7 / 5 - 840 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z + 840 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z + 840 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z + 3570 ( - 1 ) 4 / 5 z 2 / 5 + 12 ( - 1 ) 4 / 5 ( z - 1 ) 2 ( 156 z 3 + 182 z 2 + 168 z + 119 ) log ( 1 - z 5 ) + 12 ( - 1 ) 2 / 5 ( z - 1 ) 2 ( 156 z 3 + 182 z 2 + 168 z + 119 ) log ( - 1 5 z 5 + 1 ) + 1428 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 1428 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 1428 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ 7 5 6 27 5 z -1 1 9765625 z -1 2 z 22 5 -1 1309 -1 1 5 1872 1 -1 -1 2 5 z 1 5 z 5 -1 1872 -1 3 5 -1 3 5 z 1 5 1 z 5 -1 1872 -1 1 5 1 -1 -1 4 5 z 1 5 z 5 3120 -1 4 5 z 22 5 -1 1560 1 -1 -1 2 5 z 1 5 z 4 1560 -1 3 5 -1 3 5 z 1 5 1 z 4 1560 -1 1 5 1 -1 -1 4 5 z 1 5 z 4 -1 1430 -1 4 5 z 17 5 -1 480 1 -1 -1 2 5 z 1 5 z 3 480 -1 3 5 -1 3 5 z 1 5 1 z 3 480 -1 1 5 1 -1 -1 4 5 z 1 5 z 3 -1 1055 -1 4 5 z 12 5 -1 420 1 -1 -1 2 5 z 1 5 z 2 420 -1 3 5 -1 3 5 z 1 5 1 z 2 420 -1 1 5 1 -1 -1 4 5 z 1 5 z 2 -1 1080 -1 4 5 z 7 5 -1 840 1 -1 -1 2 5 z 1 5 z 840 -1 3 5 -1 3 5 z 1 5 1 z 840 -1 1 5 1 -1 -1 4 5 z 1 5 z 3570 -1 4 5 z 2 5 12 -1 4 5 z -1 2 156 z 3 182 z 2 168 z 119 1 -1 z 1 5 12 -1 2 5 z -1 2 156 z 3 182 z 2 168 z 119 -1 1 5 z 1 5 1 1428 1 -1 -1 2 5 z 1 5 -1 1428 -1 3 5 -1 3 5 z 1 5 1 -1 1428 -1 1 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