Searching for local minima and maxima. This finds the value of x which minimizes Γ(x), starting at x2. The last element of the list gives the value at which the minimum is ...

Prefix[f[expr]] prints with f[expr] given in default prefix form: f@expr. Prefix[f[expr], h] prints as hexpr.

Exact global optimization problems can be solved exactly using Minimize and Maximize. This computes the radius of the circle, centered at the origin, circumscribed about the ...

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

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

NMaximize[f, x] maximizes f numerically with respect to x.NMaximize[f, {x, y, ...}] maximizes f numerically with respect to x, y, .... NMaximize[{f, cons}, {x, y, ...}] ...

HazardFunction[dist, x] gives the hazard function for the symbolic distribution dist evaluated at x.HazardFunction[dist, {x_1, x_2, ...}] gives the multivariate hazard ...

Coth[z] gives the hyperbolic cotangent of z.

 

Series[f, {x, x_0, n}] generates a power series expansion for f about the point x = x_0 to order (x - x_0) n. Series[f, {x, x_0, n_x}, {y, y_0, n_y}, ...] successively finds ...