The following is the sequence of steps that Mathematica follows in evaluating an expression like h[e_1,e_2…]. Every time the expression changes, Mathematica effectively ...

SphericalBesselJ[n, z] gives the spherical Bessel function of the first kind j_n (z).

ExponentialGeneratingFunction[expr, n, x] gives the exponential generating function in x for the sequence whose n\[Null]^th term is given by the expression ...

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

NevilleThetaN[z, m] gives the Neville theta function \[CurlyTheta]_n (z \[VerticalSeparator] m).

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

KroneckerDelta[n_1, n_2, ...] gives the Kronecker delta \[Delta] Subscript[n, 1] Subscript[n, 2] ..., equal to 1 if all the n_i are equal, and 0 otherwise.

AiryBiZero[k] represents the k\[Null]^th zero of the Airy function Bi(x).AiryBiZero[k, x_0] represents the k\[Null]^th zero less than x_0.

Mathematica's symbolic architecture immediately defines a serializable representation for any Mathematica data or program—which can then readily be stored in a file.

Building on its core symbolic architecture, Mathematica gives immediate access to the latest in industrial-strength Boolean computation. With highly general symbolic ...