RSolve[eqn, a[n], n] solves a recurrence equation for a[n]. RSolve[{eqn_1, eqn_2, ...}, {a_1[n], a_2[n], ...}, n] solves a system of recurrence equations. RSolve[eqn, a[n_1, ...

Subfactorial[n] gives the number of permutations of n objects that leave no object fixed.

Sign[x] gives -1, 0, or 1 depending on whether x is negative, zero, or positive.

Mathematica's strengths in algebraic computation and graphics as well as numerics combine to bring unprecedented flexibility and power to geometric computation. Making ...

Mathematica's symbolic architecture allows it to represent any equation as a symbolic expression that can be manipulated using any of Mathematica's powerful collection of ...

You can use the Mathematica function DSolve to find symbolic solutions to ordinary and partial differential equations. Solving a differential equation consists essentially in ...

RandomVariate[dist] gives a pseudorandom variate from the symbolic distribution dist.RandomVariate[dist, n] gives a list of n pseudorandom variates from the symbolic ...

Continued fractions can be thought of as an alternative to digit sequences for representing numbers, based on division rather than multiplication by a base. Studied ...

SingularValueDecomposition[m] gives the singular value decomposition for a numerical matrix m as a list of matrices {u, w, v}, where w is a diagonal matrix and m can be ...

DiscreteRiccatiSolve[{a, b}, {q, r}] gives the matrix x that is the stabilizing solution of the discrete algebraic Riccati equation ConjugateTranspose[a].x.a - x - ...