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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ay6b.01

 Input Form

 Hypergeometric2F1[2/5, 4, 22/5, z] == (1/(234375 z^(17/5))) (238 (-1)^(1/5) (420 (-1)^(4/5) z^(2/5) + 435 (-1)^(4/5) z^(7/5) + 520 (-1)^(4/5) z^(12/5) + 6 (-1)^(4/5) (28 + 21 z + 24 z^2 + 52 z^3) Log[1 - z^(1/5)] + 6 (-1)^(2/5) (28 + 21 z + 24 z^2 + 52 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + 168 Log[1 - (-1)^(2/5) z^(1/5)] + 126 z Log[1 - (-1)^(2/5) z^(1/5)] + 144 z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 312 z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 168 (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] - 126 (-1)^(3/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 144 (-1)^(3/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 312 (-1)^(3/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] - 168 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)] - 126 (-1)^(1/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 144 (-1)^(1/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] - 312 (-1)^(1/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( 2 5 , 4 ; 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["2", "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["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 234375 z 17 / 5 ( 238 - 1 5 ( 312 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 - 312 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 - 312 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 520 ( - 1 ) 4 / 5 z 12 / 5 + 144 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 - 144 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 - 144 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 + 435 ( - 1 ) 4 / 5 z 7 / 5 + 126 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z - 126 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z - 126 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z + 420 ( - 1 ) 4 / 5 z 2 / 5 + 6 ( - 1 ) 4 / 5 ( 52 z 3 + 24 z 2 + 21 z + 28 ) log ( 1 - z 5 ) + 6 ( - 1 ) 2 / 5 ( 52 z 3 + 24 z 2 + 21 z + 28 ) log ( - 1 5 z 5 + 1 ) + 168 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 168 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 168 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ 2 5 4 22 5 z 1 234375 z 17 5 -1 238 -1 1 5 312 1 -1 -1 2 5 z 1 5 z 3 -1 312 -1 3 5 -1 3 5 z 1 5 1 z 3 -1 312 -1 1 5 1 -1 -1 4 5 z 1 5 z 3 520 -1 4 5 z 12 5 144 1 -1 -1 2 5 z 1 5 z 2 -1 144 -1 3 5 -1 3 5 z 1 5 1 z 2 -1 144 -1 1 5 1 -1 -1 4 5 z 1 5 z 2 435 -1 4 5 z 7 5 126 1 -1 -1 2 5 z 1 5 z -1 126 -1 3 5 -1 3 5 z 1 5 1 z -1 126 -1 1 5 1 -1 -1 4 5 z 1 5 z 420 -1 4 5 z 2 5 6 -1 4 5 52 z 3 24 z 2 21 z 28 1 -1 z 1 5 6 -1 2 5 52 z 3 24 z 2 21 z 28 -1 1 5 z 1 5 1 168 1 -1 -1 2 5 z 1 5 -1 168 -1 3 5 -1 3 5 z 1 5 1 -1 168 -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