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.bjlz.01

 Input Form

 Hypergeometric2F1[-(25/8), 6, -(1/8), z] == (1/268435456) (255 ((2048 (6679 - 12642 z + 6027 z^2))/(-1 + z)^3 - 28176225 (-(8/9) - 8 z + z^(9/8) (-Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) + 188946450 (-(8/17) - (8 z)/9 - 8 z^2 + z^(17/8) (-Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - 245630385 (-(8/25) - (8 z)/17 - (8 z^2)/9 - 8 z^3 + z^(25/8) (-Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 25 8 , 6 ; - 1 8 ; 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["25", "8"]]], 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["1", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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 268435456 ( 255 ( 2048 ( 6027 z 2 - 12642 z + 6679 ) ( z - 1 ) 3 - 28176225 ( ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 9 / 8 - 8 z - 8 9 ) + 188946450 ( ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 17 / 8 - 8 z 2 - 8 z 9 - 8 17 ) - 245630385 ( ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 25 / 8 - 8 z 3 - 8 z 2 9 - 8 z 17 - 8 25 ) ) ) HypergeometricPFQ -1 25 8 6 -1 1 8 z 1 268435456 255 2048 6027 z 2 -1 12642 z 6679 z -1 3 -1 -1 28176225 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 z 9 8 -1 8 z -1 8 9 188946450 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 z 17 8 -1 8 z 2 -1 8 z 9 -1 -1 8 17 -1 245630385 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 z 25 8 -1 8 z 3 -1 8 z 2 9 -1 -1 8 z 17 -1 -1 8 25 [/itex]

 Rule Form

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

 2007-05-02