Save["filename", symbol] appends definitions associated with the specified symbol to a file. Save["filename", " form"] appends definitions associated with all symbols whose ...

SquaresR[d, n] gives the number of ways r_d (n) to represent the integer n as a sum of d squares.

Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.

$FrontEndInitializationFunction is a function that you can assign to execute when the front end link is first established by ConnectToFrontEnd[].

InverseBetaRegularized[s, a, b] gives the inverse of the regularized incomplete beta function.

Map[f, expr] or f /@ expr applies f to each element on the first level in expr. Map[f, expr, levelspec] applies f to parts of expr specified by levelspec.

When you do long calculations, it is often convenient to give names to your intermediate results. Just as in standard mathematics, or in other computer languages, you can do ...

NMinimize[f, x] minimizes f numerically with respect to x.NMinimize[f, {x, y, ...}] minimizes f numerically with respect to x, y, .... NMinimize[{f, cons}, {x, y, ...}] ...