Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch ...

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 ...

Introduced soon after ordinary hypergeometric functions, the q functions have long been studied as theoretical generalizations of hypergeometric and other functions. ...

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 ...

MathieuSPrime[a, q, z] gives the derivative with respect to z of the odd Mathieu function with characteristic value a and parameter q.

___(three _characters) or BlankNullSequence[] is a pattern object that can stand for any sequence of zero or more Mathematica expressions. ___h or BlankNullSequence[h] can ...

Version 6.0 continued Mathematica's commitment to delivering the latest and most efficient algorithms for linear algebra, generalized to arbitrary precision and with full ...