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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(19/5), 6, -(4/5), -z] == (1/3906250) (399 (-((125 (3238 + 6171 z + 2958 z^2))/(1 + z)^3) - 1573656 (-(5/9) + (5 z)/4 + z^(9/5) (Log[1 + z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 8767512 (-(5/14) + (5 z)/9 - (5 z^2)/4 - z^(14/5) (Log[1 + z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)])) - 10151856 (-(5/19) + (5 z)/14 - (5 z^2)/9 + (5 z^3)/4 + z^(19/5) (Log[1 + z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 19 5 , 6 ; - 4 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["19", "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[RowBox[List["-", FractionBox["4", "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 3906250 ( 399 ( - 125 ( 2958 z 2 + 6171 z + 3238 ) ( z + 1 ) 3 - 1573656 ( ( log ( z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - - 1 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 9 / 5 + 5 z 4 - 5 9 ) + 8767512 ( - ( log ( z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - - 1 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 14 / 5 - 5 z 2 4 + 5 z 9 - 5 14 ) - 10151856 ( ( log ( z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - - 1 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 19 / 5 + 5 z 3 4 - 5 z 2 9 + 5 z 14 - 5 19 ) ) ) HypergeometricPFQ -1 19 5 6 -1 4 5 -1 z 1 3906250 399 -1 125 2958 z 2 6171 z 3238 z 1 3 -1 -1 1573656 z 1 5 1 -1 4 5 1 -1 -1 1 5 z 1 5 -1 -1 3 5 -1 2 5 z 1 5 1 -1 2 5 1 -1 -1 3 5 z 1 5 -1 -1 1 5 -1 4 5 z 1 5 1 z 9 5 5 z 4 -1 -1 5 9 8767512 -1 z 1 5 1 -1 4 5 1 -1 -1 1 5 z 1 5 -1 -1 3 5 -1 2 5 z 1 5 1 -1 2 5 1 -1 -1 3 5 z 1 5 -1 -1 1 5 -1 4 5 z 1 5 1 z 14 5 -1 5 z 2 4 -1 5 z 9 -1 -1 5 14 -1 10151856 z 1 5 1 -1 4 5 1 -1 -1 1 5 z 1 5 -1 -1 3 5 -1 2 5 z 1 5 1 -1 2 5 1 -1 -1 3 5 z 1 5 -1 -1 1 5 -1 4 5 z 1 5 1 z 19 5 5 z 3 4 -1 -1 5 z 2 9 -1 5 z 14 -1 -1 5 19 [/itex]

 Rule Form

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

 2007-05-02