RSolve (Built-in Mathematica Symbol)

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, ...

EllipticTheta (Built-in Mathematica Symbol)

EllipticTheta[a, u, q] gives the theta function \[CurlyTheta]_a (u, q) (a = 1, ..., 4).

Coth (Built-in Mathematica Symbol)

Coth[z] gives the hyperbolic cotangent of z.

Perform a Monte Carlo Simulation (Mathematica How To)

Monte Carlo methods use randomly generated numbers or events to simulate random processes and estimate complicated results. For example, they are used to model financial ...

AppellF1 (Built-in Mathematica Symbol)

AppellF1[a, b_1, b_2, c, x, y] is the Appell hypergeometric function of two variables F_1 (a; b_1, b_2; c; x, y).

ArcSinh (Built-in Mathematica Symbol)

ArcSinh[z] gives the inverse hyperbolic sine sinh -1 (z) of the complex number z.

ByteCount (Built-in Mathematica Symbol)

ByteCount[expr] gives the number of bytes used internally by Mathematica to store expr.

Coordinate Systems for ... (Mathematica Tutorial)

Whenever Mathematica draws a three-dimensional object, it always effectively puts a cuboidal box around the object. With the default option setting Boxed->True, Mathematica ...

DiscreteShift (Built-in Mathematica Symbol)

DiscreteShift[f, i] gives the discrete shift DiscreteShift[f(i), i] == f(i + 1). DiscreteShift[f, {i, n}] gives the multiple shift \[DiscreteShift]_i^n\ f.DiscreteShift[f, ...

Further Examples of Exactly Solvable ... (Mathematica Tutorial)

The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...