Asymptotics is the calculus of approximations. It is used to solve hard problems that cannot be solved exactly and to provide simpler forms of complicated results, from early results like Taylor's and Stirling's formulas to the prime number theorem. It is extensively used in areas such as number theory, combinatorics, numerical analysis, analysis of algorithms, probability and statistics, special functions and modern physics. The Wolfram Language makes the language of asymptotics widely available and accessible. The language design makes it easy and natural to use by a wide audience. Extensive documentation and examples make it easy to learn and use in a variety of scenarios. Advanced algorithms make it actually work for an extensive range of problems.

Asymptotic — asymptotic approximation to functions, integral transforms, etc.

DiscreteAsymptotic — asymptotic approximation to sequences, summation transforms

Asymptotic Solvers

AsymptoticIntegrate — asymptotic approximation to integrals

AsymptoticDSolveValue — asymptotic approximation to differential equations

AsymptoticSum — asymptotic approximation to sums

AsymptoticProduct — asymptotic approximation to products

AsymptoticRSolveValue — asymptotic approximation to difference equations

AsymptoticSolve — asymptotic approximation to algebraic equations

AsymptoticExpectation — asymptotic approximation to expectations

AsymptoticProbability — asymptotic approximation to probabilities

Series — asymptotic series approximation to functions

Asymptotic Relations

AsymptoticLess — give conditions for or when

AsymptoticLessEqual — give conditions for or when

AsymptoticGreaterEqual — give conditions for or when

AsymptoticGreater — give conditions for or when

AsymptoticEqual — give conditions for or when

AsymptoticEquivalent — give conditions for when

Asymptotic Limit Functions

Limit — find the univariate or multivariate limit of a function

MinLimit, MaxLimit — lower and upper limit of a function

DiscreteLimit — find the univariate or multivariate limit of a sequence

DiscreteMinLimit, DiscreteMaxLimit — lower and upper limit of a sequence