Orthogonal Polynomials (Mathematica Tutorial)

Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...

RealDigits (Built-in Mathematica Symbol)

RealDigits[x] gives a list of the digits in the approximate real number x, together with the number of digits that are to the left of the decimal point. RealDigits[x, b] ...

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 ...

Position (Built-in Mathematica Symbol)

Position[expr, pattern] gives a list of the positions at which objects matching pattern appear in expr. Position[expr, pattern, levelspec] finds only objects that appear on ...

Ratios (Built-in Mathematica Symbol)

Ratios[list] gives the successive ratios of elements in list. Ratios[list, n] gives the n\[Null]^th iterated ratios of list. Ratios[list, {n_1, n_2, ...}] gives the ...

Symbolic Graphics Language (Mathematica Guide)

Mathematica uses the powerful idea of building up all 2D and 3D graphics from symbolic primitives—which can be manipulated using all standard Mathematica functions and ...

NMinimize (Built-in Mathematica Symbol)

NMinimize[f, x] minimizes f numerically with respect to x.NMinimize[f, {x, y, ...}] minimizes f numerically with respect to x, y, .... NMinimize[{f, cons}, {x, y, ...}] ...

IntegerExponent (Built-in Mathematica Symbol)

IntegerExponent[n, b] gives the highest power of b that divides n.

WeierstrassHalfPeriods (Built-in Mathematica Symbol)

WeierstrassHalfPeriods[{g_2, g_3}] gives the half-periods {\[Omega], \[Omega]^\[Prime]} for Weierstrass elliptic functions corresponding to the invariants {g_2, g_3}.

JacobiDS (Built-in Mathematica Symbol)

JacobiDS[u, m] gives the Jacobi elliptic function ds(u | m).