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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(6/5), 4, 14/5, -z] == (1/(78125 z^(9/5))) (12 (-1)^(1/5) (3 (-1)^(4/5) (-4 + 33 z + 528 z^2 + 616 z^3) Log[1 + z^(1/5)] + 3 (-4 + 33 z + 528 z^2 + 616 z^3) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (3 (-4 + 33 z + 528 z^2 + 616 z^3) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-3 (-4 + 33 z + 528 z^2 + 616 z^3) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (3 + 1276 z + 1848 z^2) + 3 (-4 + 33 z + 528 z^2 + 616 z^3) Log[1 + (-1)^(4/5) z^(1/5)])))))

 Standard Form

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 MathML Form

 2 F 1 ( - 6 5 , 4 ; 14 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["6", "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["14", "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 78125 z 9 / 5 ( 12 - 1 5 ( 3 ( - 1 ) 4 / 5 ( 616 z 3 + 528 z 2 + 33 z - 4 ) log ( z 5 + 1 ) + 3 ( 616 z 3 + 528 z 2 + 33 z - 4 ) log ( 1 - - 1 5 z 5 ) - - 1 5 ( 3 ( 616 z 3 + 528 z 2 + 33 z - 4 ) log ( ( - 1 ) 2 / 5 z 5 + 1 ) + - 1 5 ( - 1 5 ( 5 - 1 5 z 4 / 5 ( 1848 z 2 + 1276 z + 3 ) + 3 ( 616 z 3 + 528 z 2 + 33 z - 4 ) log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) - 3 ( 616 z 3 + 528 z 2 + 33 z - 4 ) log ( 1 - ( - 1 ) 3 / 5 z 5 ) ) ) ) ) HypergeometricPFQ -1 6 5 4 14 5 -1 z 1 78125 z 9 5 -1 12 -1 1 5 3 -1 4 5 616 z 3 528 z 2 33 z -4 z 1 5 1 3 616 z 3 528 z 2 33 z -4 1 -1 -1 1 5 z 1 5 -1 -1 1 5 3 616 z 3 528 z 2 33 z -4 -1 2 5 z 1 5 1 -1 1 5 -1 1 5 5 -1 1 5 z 4 5 1848 z 2 1276 z 3 3 616 z 3 528 z 2 33 z -4 -1 4 5 z 1 5 1 -1 3 616 z 3 528 z 2 33 z -4 1 -1 -1 3 5 z 1 5 [/itex]

 Rule Form

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

 2007-05-02