Limit[expr,x->x_0] tells you what the value of expr is when x tends to x_0. When this value is infinite, it is often useful instead to know the residue of expr when x equals ...

AlternatingGroupIndex[n, x] gives the cycle index of the alternating group of size n permutations as a polynomial in the symbols x[1], x[2], ..., x[n]}.

ChromaticPolynomial[g, z] gives the chromatic polynomial P(z) of graph g, which counts the number of ways to color g with, at most, z colors.

CyclicGroupIndex[n, x] returns the cycle index of the cyclic group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

DihedralGroupIndex[n, x] returns the cycle index of the dihedral group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

MinimumVertexCover[g] finds a minimum vertex cover of graph g.

SymmetricGroupIndex[n, x] returns the cycle index of the symmetric group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

FieldIrreducible[f, s] gives the irreducible polynomial in the symbol s associated with the field f.

BSplineFunction[{pt_1, pt_2, ...}] represents a B-spline function for a curve defined by the control points pt_i.BSplineFunction[array] represents a B-spline function for a ...

DivisorSum[n, form] represents the sum of form[i] for all i that divide n.DivisorSum[n, form, cond] includes only those divisors for which cond[i] gives True.