MathieuS[a, q, z] gives the odd Mathieu function with characteristic value a and parameter q.

DifferenceRootReduce[expr, n] attempts to reduce expr to a single DifferenceRoot object as a function of n.

Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch ...

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.

GaussianIntegers is an option for FactorInteger, PrimeQ, Factor, and related functions that specifies whether factorization should be done over Gaussian integers.

PossibleZeroQ[expr] gives True if basic symbolic and numerical methods suggest that expr has value zero, and gives False otherwise.

Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using ...

LQRegulatorGains[ss, {q, r}] gives the optimal state feedback gain matrix for the StateSpaceModel object ss and the quadratic cost function with state and control weighting ...

LQOutputRegulatorGains[ss, {q, r}] gives the optimal state feedback gain matrix for the StateSpaceModel object ss and the quadratic cost function with output and control ...

ForAll[x, expr] represents the statement that expr is True for all values of x. ForAll[x, cond, expr] states that expr is True for all x satisfying the condition cond. ...