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

LegendreQ[n, z] gives the Legendre function of the second kind Q_n (z). LegendreQ[n, m, z] gives the associated Legendre function of the second kind Q_n^m(z).

Integers represents the domain of integers, as in x \[Element] Integers.

ParabolicCylinderD[\[Nu], z] gives the parabolic cylinder function D_\[Nu] (z).

There are many situations where one wants to find a formula that best fits a given set of data. One way to do this in Mathematica is to use Fit. Basic linear fitting. Here is ...

Reals represents the domain of real numbers, as in x \[Element] Reals.

FindLinearRecurrence[list] finds if possible the minimal linear recurrence that generates list.FindLinearRecurrence[list, d] finds if possible the linear recurrence of ...

In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...

ToRadicals[expr] attempts to express all Root objects in expr in terms of radicals.

Any combination of equations or inequalities can be thought of as implicitly defining a region in some kind of space. The fundamental function of Reduce is to turn this type ...