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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(6/5), 3, 24/5, -z] == (1/(3906250 z^(19/5))) (399 (-1)^(1/5) (12 (-1)^(4/5) (1 + z)^3 (63 - 99 z + 88 z^2) Log[1 + z^(1/5)] + 12 (1 + z)^3 (63 - 99 z + 88 z^2) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (12 (1 + z)^3 (63 - 99 z + 88 z^2) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-12 (1 + z)^3 (63 - 99 z + 88 z^2) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-189 - 186 z + 126 z^2 + 1804 z^3 + 1056 z^4) + 12 (1 + z)^3 (63 - 99 z + 88 z^2) Log[1 + (-1)^(4/5) z^(1/5)])))))

 Standard Form

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 MathML Form

 2 F 1 ( - 6 5 , 3 ; 24 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["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["24", "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 z 19 / 5 ( 399 - 1 5 ( 12 ( - 1 ) 4 / 5 ( 88 z 2 - 99 z + 63 ) log ( z 5 + 1 ) ( z + 1 ) 3 + 12 ( 88 z 2 - 99 z + 63 ) log ( 1 - - 1 5 z 5 ) ( z + 1 ) 3 - - 1 5 ( 12 ( 88 z 2 - 99 z + 63 ) log ( ( - 1 ) 2 / 5 z 5 + 1 ) ( z + 1 ) 3 + - 1 5 ( - 1 5 ( 12 ( 88 z 2 - 99 z + 63 ) log ( ( - 1 ) 4 / 5 z 5 + 1 ) ( z + 1 ) 3 + 5 - 1 5 z 4 / 5 ( 1056 z 4 + 1804 z 3 + 126 z 2 - 186 z - 189 ) ) - 12 ( z + 1 ) 3 ( 88 z 2 - 99 z + 63 ) log ( 1 - ( - 1 ) 3 / 5 z 5 ) ) ) ) ) HypergeometricPFQ -1 6 5 3 24 5 -1 z 1 3906250 z 19 5 -1 399 -1 1 5 12 -1 4 5 88 z 2 -1 99 z 63 z 1 5 1 z 1 3 12 88 z 2 -1 99 z 63 1 -1 -1 1 5 z 1 5 z 1 3 -1 -1 1 5 12 88 z 2 -1 99 z 63 -1 2 5 z 1 5 1 z 1 3 -1 1 5 -1 1 5 12 88 z 2 -1 99 z 63 -1 4 5 z 1 5 1 z 1 3 5 -1 1 5 z 4 5 1056 z 4 1804 z 3 126 z 2 -1 186 z -189 -1 12 z 1 3 88 z 2 -1 99 z 63 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