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

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 ...

Mathematica contains some powerful primitives for making structural changes to expressions. You can use these primitives both to implement mathematical properties such as ...

The raw SQL command UPDATE updates data in a database. An alternative is to use the Mathematica command SQLUpdate, described in "Updating Data". If you find that the examples ...

An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...

BSplineCurve[{pt_1, pt_2, ...}] is a graphics primitive that represents a non-uniform rational B-spline curve with control points pt_i.

SparseArray[{pos_1 -> val_1, pos_2 -> val_2, ...}] yields a sparse array in which values val_i appear at positions pos_i. SparseArray[{pos_1, pos_2, ...} -> {val_1, val_2, ...

CUDA is a general C-like programming developed by NVIDIA to program Graphical Processing Units (GPUs). CUDALink provides an easy interface to program the GPU by removing many ...

ListPolarPlot[{r_1, r_2, ...}] plots points equally spaced in angle at radii r_i.ListPolarPlot[{{\[Theta]_1, r_1}, {\[Theta]_2, r_2}, ...}] plots points at polar coordinates ...

The functions described here are among the most commonly used continuous univariate statistical distributions. You can compute their densities, means, variances, and other ...