Ceiling (Built-in Mathematica Symbol)

Ceiling[x] gives the smallest integer greater than or equal to x. Ceiling[x, a] gives the smallest multiple of a greater than or equal to x.

Factorial2 (Built-in Mathematica Symbol)

n!! gives the double factorial of n.

FixedPoint (Built-in Mathematica Symbol)

FixedPoint[f, expr] starts with expr, then applies f repeatedly until the result no longer changes.

GCD (Built-in Mathematica Symbol)

GCD[n_1, n_2, ...] gives the greatest common divisor of the n_i.

GegenbauerC (Built-in Mathematica Symbol)

GegenbauerC[n, m, x] gives the Gegenbauer polynomial C_n^(m)(x). GegenbauerC[n, x] gives the renormalized form lim_(m->0) C_n^(m)(x)/m.

Hypergeometric1F1 (Built-in Mathematica Symbol)

Hypergeometric1F1[a, b, z] is the Kummer confluent hypergeometric function \[Null]_1 F_1 (a; b; z).

LaguerreL (Built-in Mathematica Symbol)

LaguerreL[n, x] gives the Laguerre polynomial L_n (x). LaguerreL[n, a, x] gives the generalized Laguerre polynomial L_n^a(x).

LCM (Built-in Mathematica Symbol)

LCM[n_1, n_2, ...] gives the least common multiple of the n_i.

ModularLambda (Built-in Mathematica Symbol)

ModularLambda[\[Tau]] gives the modular lambda elliptic function \[Lambda](\[Tau]).

Quotient (Built-in Mathematica Symbol)

Quotient[m, n] gives the integer quotient of m and n. Quotient[m, n, d] uses an offset d.