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

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, ...

Casoratian[{y_1, y_2, ...}, n] gives the Casoratian determinant for the sequences y_1, y_2, ... depending on n.Casoratian[eqn, y, n] gives the Casoratian determinant for the ...

Mathematica has been used to make many important discoveries in discrete mathematics over the past two decades. Its integration of highly efficient and often original ...

SumConvergence[f, n] gives conditions for the sum \[Sum]_n^\[Infinity] f to be convergent.SumConvergence[f, {n_1, n_2, ...}] gives conditions for the multiple sum \[Sum]_n ...

ZTransform[expr, n, z] gives the Z transform of expr. ZTransform[expr, {n_1, n_2, ...}, {z_1, z_2, ...}] gives the multidimensional Z transform of expr.

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...

DiscreteConvolve[f, g, n, m] gives the convolution with respect to n of the expressions f and g. DiscreteConvolve[f, g, {n_1, n_2, ...}, {m_1, m_2, ...}] gives the ...

InverseZTransform[expr, z, n] gives the inverse Z transform of expr. InverseZTransform[expr, {z_1, z_2, ...}, {n_1, n_2, ...}] gives the multiple inverse Z transform of expr.

SpheroidalEigenvalue[n, m, \[Gamma]] gives the spheroidal eigenvalue with degree n and order m.