MomentConvert[mexpr, form] converts the moment expression mexpr to the specified form.

When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

MathieuCharacteristicA[r, q] gives the characteristic value a_r for even Mathieu functions with characteristic exponent r and parameter q.

MathieuCharacteristicB[r, q] gives the characteristic value b_r for odd Mathieu functions with characteristic exponent r and parameter q.

RamanujanTauZ[t] gives the Ramanujan tau Z-function Z(t).

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.

It is often useful to be able to detect and precisely locate a change in a differential system. For example, with the detection of a singularity or state change, the ...

NIntegrate[f, {x, x_min, x_max}] gives a numerical approximation to the integral \[Integral]_x_min^x_max\ f\ d \ x. NIntegrate[f, {x, x_min, x_max}, {y, y_min, y_max}, ...] ...

Product[f, {i, i_max}] evaluates the product \[Product]i = 1 i_max f. Product[f, {i, i_min, i_max}] starts with i = i_min. Product[f, {i, i_min, i_max, di}] uses steps di. ...

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. ...