Function[body] or body & is a pure function. The formal parameters are # (or #1), #2, etc. Function[x, body] is a pure function with a single formal parameter x. ...

Limit[expr, x -> x_0] finds the limiting value of expr when x approaches x_0.

Pochhammer[a, n] gives the Pochhammer symbol (a) n.

Mathematica 6.0 fundamentally redefined Mathematica and introduced a major new paradigm for computation. Building on Mathematica's time-tested core symbolic architecture, ...

SetPrecision[expr, p] yields a version of expr in which all numbers have been set to have precision p.

Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using ...

Solve[expr, vars] attempts to solve the system expr of equations or inequalities for the variables vars. Solve[expr, vars, dom] solves over the domain dom. Common choices of ...

FullSimplify[expr] tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds. FullSimplify[expr, assum] ...

Mathematica has over 3000 built-in functions and other objects, all based on a single unified framework, and all carefully designed to work together, both in simple ...

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...