Mathematica allows you to define transformation rules for any expression. You can define such rules not only for functions that you add to Mathematica, but also for intrinsic ...

Many programs you write will involve operations that need to be iterated several times. Nest and NestList are powerful constructs for doing this. Applying functions of one ...

Some common operations on special functions. Most special functions have simpler forms when given certain specific arguments. Mathematica will automatically simplify special ...

Although Mathematica matches patterns in a purely structural fashion, its notion of structural equivalence is quite sophisticated. In particular, it takes account of ...

Mathematica has a wide coverage of named functions defined by sums and recurrence relations. Often using original algorithms developed at Wolfram Research, Mathematica ...

In many kinds of numerical computations, it is convenient to introduce approximate functions. Approximate functions can be thought of as generalizations of ordinary ...

Mathieu and related functions. The Mathieu functions MathieuC[a,q,z] and MathieuS[a,q,z] are solutions to the equation y^′′+[a-2qcos(2z)]y0. This equation appears in many ...

Mathematica contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.

Mathematica's sophisticated algorithms for handling higher mathematical functions to arbitrary precision—and in symbolic form—immediately brings a new level of accuracy—and ...

Mathematica offers multiple ways of plotting functions of one variable. These include ordinary plots, log plots, parametric plots, and polar plots.