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; }

 JacobiSN

 http://functions.wolfram.com/09.36.13.0004.01

 Input Form

 4 m w[z, m]^4 Derivative[1, 0][w][z, m]^4 - w[z, m]^2 Derivative[1, 0][w][z, m]^2 (8 (-1 + m) m Derivative[1, 0][w][z, m] Derivative[1, 1][w][z, m] + Derivative[2, 0][w][z, m] (-8 (-1 + m) m Derivative[0, 1][w][z, m] + Derivative[2, 0][w][z, m])) + 2 (-1 + m) (Derivative[1, 0][w][z, m] Derivative[1, 1][w][z, m] - Derivative[0, 1][w][z, m] Derivative[2, 0][w][z, m]) (2 (-1 + m) m Derivative[1, 0][w][z, m] Derivative[1, 1][w][z, m] + Derivative[2, 0][w][z, m] (-2 (-1 + m) m Derivative[0, 1][w][z, m] + Derivative[2, 0][w][z, m])) == 0 /; w[z, m] == JacobiSN[z, m]

 Standard Form

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 MathML Form

 4 m w ( z , m ) 4 w ( 1 , 0 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "0"]], ")"]], Derivative] ( z , m ) 4 - w ( z , m ) 2 ( 8 ( m - 1 ) m w ( 1 , 0 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "0"]], ")"]], Derivative] ( z , m ) w ( 1 , 1 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "1"]], ")"]], Derivative] ( z , m ) + w ( 2 , 0 ) TagBox[RowBox[List["(", RowBox[List["2", ",", "0"]], ")"]], Derivative] ( z , m ) ( w ( 2 , 0 ) TagBox[RowBox[List["(", RowBox[List["2", ",", "0"]], ")"]], Derivative] ( z , m ) - 8 ( m - 1 ) m w ( 0 , 1 ) TagBox[RowBox[List["(", RowBox[List["0", ",", "1"]], ")"]], Derivative] ( z , m ) ) ) w ( 1 , 0 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "0"]], ")"]], Derivative] ( z , m ) 2 + 2 ( m - 1 ) ( w ( 1 , 0 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "0"]], ")"]], Derivative] ( z , m ) w ( 1 , 1 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "1"]], ")"]], Derivative] ( z , m ) - w ( 0 , 1 ) TagBox[RowBox[List["(", RowBox[List["0", ",", "1"]], ")"]], Derivative] ( z , m ) w ( 2 , 0 ) TagBox[RowBox[List["(", RowBox[List["2", ",", "0"]], ")"]], Derivative] ( z , m ) ) ( 2 ( m - 1 ) m w ( 1 , 0 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "0"]], ")"]], Derivative] ( z , m ) w ( 1 , 1 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "1"]], ")"]], Derivative] ( z , m ) + w ( 2 , 0 ) TagBox[RowBox[List["(", RowBox[List["2", ",", "0"]], ")"]], Derivative] ( z , m ) ( w ( 2 , 0 ) TagBox[RowBox[List["(", RowBox[List["2", ",", "0"]], ")"]], Derivative] ( z , m ) - 2 ( m - 1 ) m w ( 0 , 1 ) TagBox[RowBox[List["(", RowBox[List["0", ",", "1"]], ")"]], Derivative] ( z , m ) ) ) 0 /; w ( z , m ) sn ( z m ) Condition 4 m w z m 4 1 0 w z m 4 -1 w z m 2 8 m -1 m 1 0 w z m 1 1 w z m 2 0 w z m 2 0 w z m -1 8 m -1 m 0 1 w z m 1 0 w z m 2 2 m -1 1 0 w z m 1 1 w z m -1 0 1 w z m 2 0 w z m 2 m -1 m 1 0 w z m 1 1 w z m 2 0 w z m 2 0 w z m -1 2 m -1 m 0 1 w z m 0 w z m JacobiSN z m [/itex]

 Rule Form

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

 2007-05-02