EllipticF (Built-in Mathematica Symbol)

EllipticF[\[Phi], m] gives the elliptic integral of the first kind F(\[Phi] \[VerticalSeparator] m).

Eigensystem (Built-in Mathematica Symbol)

Eigensystem[m] gives a list {values, vectors} of the eigenvalues and eigenvectors of the square matrix m. Eigensystem[{m, a}] gives the generalized eigenvalues and ...

Some Notes on Internal Implementation (Mathematica Tutorial)

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...

Animate (Built-in Mathematica Symbol)

Animate[expr, {u, u_min, u_max}] generates an animation of expr in which u varies continuously from u_min to u_max. Animate[expr, {u, u_min, u_max, du}] takes u to vary in ...

Compile (Built-in Mathematica Symbol)

Compile[{x_1, x_2, ...}, expr] creates a compiled function that evaluates expr assuming numerical values of the x_i. Compile[{{x_1, t_1}, ...}, expr] assumes that x_i is of a ...

InterpolatingPolynomial (Built-in Mathematica Symbol)

InterpolatingPolynomial[{f_1, f_2, ...}, x] constructs an interpolating polynomial in x which reproduces the function values f_i at successive integer values 1, 2, ... of x. ...

ProductLog (Built-in Mathematica Symbol)

ProductLog[z] gives the principal solution for w in z == w e^w. ProductLog[k, z] gives the k\[Null]^th solution.

RotationTransform (Built-in Mathematica Symbol)

RotationTransform[\[Theta]] gives a TransformationFunction that represents a rotation in 2D by \[Theta] radians about the origin.RotationTransform[\[Theta], p] gives a 2D ...

ColorData (Built-in Mathematica Symbol)

ColorData["scheme"] gives a function that generates colors in the named color scheme when applied to parameter values. ColorData["scheme", " property"] gives the specified ...

EllipticE (Built-in Mathematica Symbol)

EllipticE[m] gives the complete elliptic integral E(m). EllipticE[\[Phi], m] gives the elliptic integral of the second kind E(\[Phi] \[VerticalSeparator] m).