BesselJ (Built-in Mathematica Symbol)

BesselJ[n, z] gives the Bessel function of the first kind J_n (z).

CoefficientList (Built-in Mathematica Symbol)

CoefficientList[poly, var] gives a list of coefficients of powers of var in poly, starting with power 0. CoefficientList[poly, {var_1, var_2, ...}] gives an array of ...

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.

Inverse (Built-in Mathematica Symbol)

Inverse[m] gives the inverse of a square matrix m.

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).

LegendreQ (Built-in Mathematica Symbol)

LegendreQ[n, z] gives the Legendre function of the second kind Q_n (z). LegendreQ[n, m, z] gives the associated Legendre function of the second kind Q_n^m(z).

SetSharedVariable (Built-in Mathematica Symbol)

SetSharedVariable[s_1, s_2, ...] declares the symbols s_i as shared variables whose values are synchronized among all parallel kernels.

SpheroidalPS (Built-in Mathematica Symbol)

SpheroidalPS[n, m, \[Gamma], z] gives the angular spheroidal function PS n, m (\[Gamma], z) of the first kind.

References (Mathematica Tutorial)

[AB04] Abell, M. L. and J. P. Braselton. Differential Equations with Mathematica. (3rd ed.) Elsevier Academic Press, 2004. [A89] Abramov, S. A. "Rational Solutions of Linear ...

Matrix Inversion (Mathematica Tutorial)

Matrix inversion. Here is a simple 2×2 matrix. This gives the inverse of m. In producing this formula, Mathematica implicitly assumes that the determinant ad-bc is nonzero.