MedianFilter[image, r] filters image by replacing every value by the median in its range r neighborhood. MedianFilter[data, r] applies median filtering to an array of data.

Mathematica usually goes about its work silently, giving output only when it has finished doing the calculations you asked for. However, if it looks as if Mathematica is ...

Exists[x, expr] represents the statement that there exists a value of x for which expr is True. Exists[x, cond, expr] states that there exists an x satisfying the condition ...

TrigReduce[expr] rewrites products and powers of trigonometric functions in expr in terms of trigonometric functions with combined arguments.

EconomizedRationalApproximation[expr, {x, {x_0, x_1}, m, n}] gives the economized rational approximation to expr that is good over the interval x_0 to x_1, with numerator ...

Numerical sums and products. This gives a numerical approximation to ∑_(i=1)^∞((1)/(i^3+i!)). There is no exact result for this sum, so Mathematica leaves it in a symbolic ...

NecklacePolynomial[n, c, Cyclic] returns a polynomial in the colors in c whose coefficients represent numbers of ways of coloring an n-bead necklace with colors chosen from ...

New functions SymmetricPolynomial and SymmetricReduction have been added to the built-in Mathematica kernel.

Tan[z] gives the tangent of z.

TreePlot[{v i 1 -> v j 1, v i 2 -> v j 2, ...}] generates a tree plot of the graph in which vertex v_ik is connected to vertex v_jk.TreePlot[{{v i 1 -> v j 1, lbl_1}, ...}] ...