html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(18/5), 5, 2/5, -z] == (1/390625) (234 (625/(1 + z) - 7176 (-(5/3) + z^(3/5) (Log[1 + z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 75348 (-(5/8) + (5 z)/3 - z^(8/5) (Log[1 + z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)])) - 191268 (-(5/13) + (5 z)/8 - (5 z^2)/3 + z^(13/5) (Log[1 + z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 134596 (-(5/18) + (5 z)/13 - (5 z^2)/8 + (5 z^3)/3 - z^(18/5) (Log[1 + z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 18 5 , 5 ; 2 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["18", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["2", "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 390625 ( 234 ( - 7176 ( z 3 / 5 ( log ( z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - - 1 5 z 5 ) - - 1 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) - 5 3 ) + 75348 ( - ( log ( z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - - 1 5 z 5 ) - - 1 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 8 / 5 + 5 z 3 - 5 8 ) - 191268 ( ( log ( z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - - 1 5 z 5 ) - - 1 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 13 / 5 - 5 z 2 3 + 5 z 8 - 5 13 ) + 134596 ( - ( log ( z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - - 1 5 z 5 ) - - 1 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 18 / 5 + 5 z 3 3 - 5 z 2 8 + 5 z 13 - 5 18 ) + 625 z + 1 ) ) HypergeometricPFQ -1 18 5 5 2 5 -1 z 1 390625 234 -7176 z 3 5 z 1 5 1 -1 -1 3 5 1 -1 -1 1 5 z 1 5 -1 -1 1 5 -1 2 5 z 1 5 1 -1 4 5 1 -1 -1 3 5 z 1 5 -1 2 5 -1 4 5 z 1 5 1 -1 5 3 75348 -1 z 1 5 1 -1 -1 3 5 1 -1 -1 1 5 z 1 5 -1 -1 1 5 -1 2 5 z 1 5 1 -1 4 5 1 -1 -1 3 5 z 1 5 -1 2 5 -1 4 5 z 1 5 1 z 8 5 5 z 3 -1 -1 5 8 -1 191268 z 1 5 1 -1 -1 3 5 1 -1 -1 1 5 z 1 5 -1 -1 1 5 -1 2 5 z 1 5 1 -1 4 5 1 -1 -1 3 5 z 1 5 -1 2 5 -1 4 5 z 1 5 1 z 13 5 -1 5 z 2 3 -1 5 z 8 -1 -1 5 13 134596 -1 z 1 5 1 -1 -1 3 5 1 -1 -1 1 5 z 1 5 -1 -1 1 5 -1 2 5 z 1 5 1 -1 4 5 1 -1 -1 3 5 z 1 5 -1 2 5 -1 4 5 z 1 5 1 z 18 5 5 z 3 3 -1 -1 5 z 2 8 -1 5 z 13 -1 -1 5 18 625 z 1 -1 [/itex]

 Rule Form

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

 2007-05-02