Frequently, physical systems exhibit special symmetries or structures that make a particular coordinate system especially useful. In a mathematically elegant solution to ...

ArcLengthFactor[{f_1, f_2, f_3}, t] gives the derivative of the arc length of the curve described by the parametrized curve coordinates {f_1, f_2, f_3} with respect to the ...

ND[expr, x, x_0] gives a numerical approximation to the derivative of expr with respect to x at the point x_0.ND[expr, {x, n}, x_0] gives a numerical approximation to the ...

LerchPhi[z, s, a] gives the Lerch transcendent \[CapitalPhi] (z, s, a).

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...

StieltjesGamma[n] gives the Stieltjes constant \[Gamma]_n. StieltjesGamma[n, a] gives the generalized Stieltjes constant \[Gamma]_n (a).

InverseGudermannian[z] gives the inverse Gudermannian function gd -1 (z).

SpheroidalS1Prime[n, m, \[Gamma], z] gives the derivative with respect to z of the radial spheroidal function S_n^m, (1)(\[Gamma], z) of the first kind.

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, The derivatives of the dependent variables x are expressed explicitly in ...

Collect[expr, x] collects together terms involving the same powers of objects matching x. Collect[expr, {x_1, x_2, ...}] collects together terms that involve the same powers ...