Lists are central constructs in Mathematica, used to represent collections, arrays, sets, and sequences of all kinds. Lists can have any structure and size, and can routinely ...

Rationalize[x] converts an approximate number x to a nearby rational with small denominator. Rationalize[x, dx] yields the rational number with smallest denominator that lies ...

EllipticK[m] gives the complete elliptic integral of the first kind K(m).

Quantile[list, q] gives the q\[Null]\[Null]^th quantile of list. Quantile[list, {q_1, q_2, ...}] gives a list of quantiles q_1, q_2, .... Quantile[list, q, {{a, b}, {c, d}}] ...

Mathematica allows you to perform many operations on power series. In all cases, Mathematica gives results only to as many terms as can be justified from the accuracy of your ...

Numerical integration functions. This finds a numerical approximation to the integral ∫_(0)^∞ e^-x^3 x. Here is the numerical value of the double integral ∫_(-1)^1 dx ...

PartitionsQ[n] gives the number q (n) of partitions of the integer n into distinct parts.

WaveletPsi[wave, x] gives the wavelet function \[Psi](x) for the symbolic wavelet wave evaluated at x.WaveletPsi[wave] gives the wavelet function as a pure function.

When you make a sequence of definitions in Mathematica, some may be more general than others. Mathematica follows the principle of trying to put more general definitions ...

NSum[f, {i, i_min, i_max}] gives a numerical approximation to the sum \[Sum]i = i_min i_max f.NSum[f, {i, i_min, i_max, di}] uses a step di in the sum.