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.

ListConvolve[ker, list] forms the convolution of the kernel ker with list. ListConvolve[ker, list, k] forms the cyclic convolution in which the k\[Null]^th element of ker is ...

KarhunenLoeveDecomposition[{a_1, a_2, ...}] gives the Karhunen\[Dash]Loeve transform {b_1, b_2, ...} of the numerical arrays {a_1, a_2, ...} and the transformation matrix m, ...

Threshold[data] thresholds data by replacing values close to zero by zero.Threshold[data, tspec] thresholds data using threshold specification tspec.Threshold[image, ...] ...

A "How to" describes how to carry out particular tasks with Mathematica, giving step-by-step instructions for common cases.

NHoldAll is an attribute which specifies that none of the arguments to a function should be affected by N.

The built-in functions of Mathematica implement a very large number of algorithms from computer science and mathematics. Some of these algorithms are fairly old, but the vast ...