Pure functions. When you use functional operations such as Nest and Map, you always have to specify a function to apply. In all the examples above, we have used the "name" of ...

Turning conditions into numbers. Boole[expr] is a basic function that turns True and False into 1 and 0. It is sometimes known as the characteristic function or indicator ...

Hundreds of thousands of mathematical results derived at Wolfram Research give Mathematica unprecedented strength in the transformation and simplification of hypergeometric ...

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

Mathematica contains hundreds of original algorithms for computing integer functions involving integers of any size.

Mathematica includes all the common special functions of mathematical physics found in standard handbooks. Each of the various classes of functions is discussed in turn. One ...

AlgebraicUnitQ[a] yields True if a is an algebraic unit, and yields False otherwise.

With careful standardization of argument conventions, Mathematica provides full coverage of all standard types of elliptic functions, with arbitrary-precision numerical ...

Functions relating real numbers and integers. Extracting integer and fractional parts. IntegerPart[x] and FractionalPart[x] can be thought of as extracting digits to the left ...

Combinatorial functions. The factorial function n! gives the number of ways of ordering n objects. For non-integer n, the numerical value of n! is obtained from the gamma ...