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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b00w.01

 Input Form

 Hypergeometric2F1[7/5, 3, 22/5, -z] == (1/(3125 z^(17/5))) (714 (-1)^(1/5) (-105 (-1)^(4/5) z^(2/5) - 5 (-1)^(4/5) z^(7/5) + (-1)^(4/5) (-42 - 14 z + 3 z^2) Log[1 + z^(1/5)] + (-1)^(2/5) (-42 - 14 z + 3 z^2) Log[1 - (-1)^(1/5) z^(1/5)] - 42 Log[1 + (-1)^(2/5) z^(1/5)] - 14 z Log[1 + (-1)^(2/5) z^(1/5)] + 3 z^2 Log[1 + (-1)^(2/5) z^(1/5)] + 42 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + 14 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] - 3 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 42 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] + 14 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 3 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( 7 5 , 3 ; 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["7", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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[RowBox[List["-", "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 3125 z 17 / 5 ( 714 - 1 5 ( 3 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 - 3 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 - 3 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 - 5 ( - 1 ) 4 / 5 z 7 / 5 - 14 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z + 14 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z + 14 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z - 105 ( - 1 ) 4 / 5 z 2 / 5 + ( - 1 ) 4 / 5 ( 3 z 2 - 14 z - 42 ) log ( z 5 + 1 ) + ( - 1 ) 2 / 5 ( 3 z 2 - 14 z - 42 ) log ( 1 - - 1 5 z 5 ) - 42 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + 42 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 42 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ 7 5 3 22 5 -1 z 1 3125 z 17 5 -1 714 -1 1 5 3 -1 2 5 z 1 5 1 z 2 -1 3 -1 3 5 1 -1 -1 3 5 z 1 5 z 2 -1 3 -1 1 5 -1 4 5 z 1 5 1 z 2 -1 5 -1 4 5 z 7 5 -1 14 -1 2 5 z 1 5 1 z 14 -1 3 5 1 -1 -1 3 5 z 1 5 z 14 -1 1 5 -1 4 5 z 1 5 1 z -1 105 -1 4 5 z 2 5 -1 4 5 3 z 2 -1 14 z -42 z 1 5 1 -1 2 5 3 z 2 -1 14 z -42 1 -1 -1 1 5 z 1 5 -1 42 -1 2 5 z 1 5 1 42 -1 3 5 1 -1 -1 3 5 z 1 5 42 -1 1 5 -1 4 5 z 1 5 1 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02