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; }

 PolyLog

 http://functions.wolfram.com/10.09.13.0003.01

 Input Form

 (-1 + p + z) Derivative[1][w][z]^2 + z Derivative[1][w][z] (2 (15 (-1 + z) + p (7 + 4 z)) Derivative[2][w][z] + z ((50 (-1 + z) + p (-15 + 46 z)) Derivative[3][w][z] + z ((20 (-1 + z) + p (-35 + 46 z)) Derivative[4][w][z] + z ((-2 - 12 p + 2 z + 13 p z) Derivative[5][w][z] + p (-1 + z) z Derivative[6][w][z])))) + z^2 ((p (113 - 8 z) + 225 (-1 + z)) Derivative[2][w][z]^2 + z^2 ((p (235 - 85 z) + 625 (-1 + z)) Derivative[3][w][z]^2 + z^2 (-5 (20 - 9 p - 20 z + 7 p z) Derivative[4][w][z]^2 + z^2 (-1 + p + z - p z) Derivative[5][w][z]^2 + z Derivative[4][w][z] ((p (6 - 5 z) + 20 (-1 + z)) Derivative[5][w][z] + p (-1 + z) z Derivative[6][w][z])) + z Derivative[3][w][z] (-5 (-100 (-1 + z) + p (-21 + 4 z)) Derivative[4][w][z] + 2 z ((-25 - 17 p + 25 z + 20 p z) Derivative[5][w][z] + 3 p (-1 + z) z Derivative[6][w][z]))) + z Derivative[2][w][z] ((750 (-1 + z) + p (199 + 66 z)) Derivative[3][w][z] + z ((300 (-1 + z) + p (-101 + 186 z)) Derivative[4][w][z] + z ((-30 - 68 p + 30 z + 75 p z) Derivative[5][w][z] + 7 p (-1 + z) z Derivative[6][w][z])))) == 0 /; w[z] == PolyLog[4, p, z]

 Standard Form

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 MathML Form

 ( ( ( - 5 ( 7 z p - 9 p - 20 z + 20 ) w ( 4 ) TagBox[RowBox[List["(", "4", ")"]], Derivative] ( z ) 2 + z ( ( 20 ( z - 1 ) + p ( 6 - 5 z ) ) w ( 5 ) TagBox[RowBox[List["(", "5", ")"]], Derivative] ( z ) + p ( z - 1 ) z w ( 6 ) TagBox[RowBox[List["(", "6", ")"]], Derivative] ( z ) ) w ( 4 ) TagBox[RowBox[List["(", "4", ")"]], Derivative] ( z ) + z 2 ( - z p + p + z - 1 ) w ( 5 ) TagBox[RowBox[List["(", "5", ")"]], Derivative] ( z ) 2 ) z 2 + w ( 3 ) TagBox[RowBox[List["(", "3", ")"]], Derivative] ( z ) ( 2 z ( ( 20 z p - 17 p + 25 z - 25 ) w ( 5 ) TagBox[RowBox[List["(", "5", ")"]], Derivative] ( z ) + 3 p ( z - 1 ) z w ( 6 ) TagBox[RowBox[List["(", "6", ")"]], Derivative] ( z ) ) - 5 ( p ( 4 z - 21 ) - 100 ( z - 1 ) ) w ( 4 ) TagBox[RowBox[List["(", "4", ")"]], Derivative] ( z ) ) z + ( 625 ( z - 1 ) + p ( 235 - 85 z ) ) w ( 3 ) TagBox[RowBox[List["(", "3", ")"]], Derivative] ( z ) 2 ) z 2 + w ′′ ( z ) ( ( 750 ( z - 1 ) + p ( 66 z + 199 ) ) w ( 3 ) TagBox[RowBox[List["(", "3", ")"]], Derivative] ( z ) + z ( ( 300 ( z - 1 ) + p ( 186 z - 101 ) ) w ( 4 ) TagBox[RowBox[List["(", "4", ")"]], Derivative] ( z ) + z ( ( 75 z p - 68 p + 30 z - 30 ) w ( 5 ) TagBox[RowBox[List["(", "5", ")"]], Derivative] ( z ) + 7 p ( z - 1 ) z w ( 6 ) TagBox[RowBox[List["(", "6", ")"]], Derivative] ( z ) ) ) ) z + ( 225 ( z - 1 ) + p ( 113 - 8 z ) ) w ′′ ( z ) 2 ) z 2 + w ( z ) ( 2 ( 15 ( z - 1 ) + p ( 4 z + 7 ) ) w ′′ ( z ) + z ( ( 50 ( z - 1 ) + p ( 46 z - 15 ) ) w ( 3 ) TagBox[RowBox[List["(", "3", ")"]], Derivative] ( z ) + z ( ( 20 ( z - 1 ) + p ( 46 z - 35 ) ) w ( 4 ) TagBox[RowBox[List["(", "4", ")"]], Derivative] ( z ) + z ( ( 13 z p - 12 p + 2 z - 2 ) w ( 5 ) TagBox[RowBox[List["(", "5", ")"]], Derivative] ( z ) + p ( z - 1 ) z w ( 6 ) TagBox[RowBox[List["(", "6", ")"]], Derivative] ( z ) ) ) ) ) z + ( p + z - 1 ) w ( z ) 2 0 /; w ( z ) S PolyLog 4 , p ( z ) Condition -5 7 z p -1 9 p -1 20 z 20 z 4 w z 2 z 20 z -1 p 6 -1 5 z z 5 w z p z -1 z z 6 w z z 4 w z z 2 -1 z p p z -1 z 5 w z 2 z 2 z 3 w z 2 z 20 z p -1 17 p 25 z -25 z 5 w z 3 p z -1 z z 6 w z -1 5 p 4 z -21 -1 100 z -1 z 4 w z z 625 z -1 p 235 -1 85 z z 3 w z 2 z 2 z 2 w z 750 z -1 p 66 z 199 z 3 w z z 300 z -1 p 186 z -101 z 4 w z z 75 z p -1 68 p 30 z -30 z 5 w z 7 p z -1 z z 6 w z z 225 z -1 p 113 -1 8 z z 2 w z 2 z 2 z w z 2 15 z -1 p 4 z 7 z 2 w z z 50 z -1 p 46 z -15 z 3 w z z 20 z -1 p 46 z -35 z 4 w z z 13 z p -1 12 p 2 z -2 z 5 w z p z -1 z z 6 w z z p z -1 z w z 2 0 w z PolyLog 4 p z [/itex]

 Rule Form

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

 2007-05-02