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 ...

New functions CountRoots, IsolatingInterval, and RootIntervals have been added to the built-in Mathematica kernel. IsolatingInterval includes the functionality of ...

LucasL[n] gives the Lucas number L_n.LucasL[n, x] gives the Lucas polynomial L_n (x).

Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

PowerModList[a, s/r, m] gives a list of all x modulo m for which x^r \[Congruent] a^s mod m.

Mathematica normally assumes that variables which appear in equations can stand for arbitrary complex numbers. But when you use Reduce, you can explicitly tell Mathematica ...

InverseSeries[s] takes the series s, and gives a series for the inverse of the function represented by s. InverseSeries[s, x] uses the variable x in the inverse series.

RiemannSiegelTheta[t] gives the Riemann\[Dash]Siegel function \[CurlyTheta](t).

In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced ...

The functions FindMinimum, FindMaximum, and FindRoot have the HoldAll attribute and so have special semantics for evaluation of their arguments. First, the variables are ...