# Discrete Calculus

Discrete calculus is the calculus of sequences, a.k.a. discrete time signals. Discrete calculus is the foundation for continuous calculus and used to derive numerical algorithms for it. It is the calculus used for discrete-time signal processing, discrete-time control systems and digital image processing. It is also a calculus used for combinatorics, discrete probability, finance and analysis of algorithms.  The Wolfram Language provides extensive coverage of discrete calculus and its applications. A large library of special sequences and sequence guessing from data. State-of-the-art solvers for sums, difference equations and many more. Full support for the its many application domains from signal processing and control systems to probability and number theory.

### Special Sequences »

LinearRecurrence generate a linear recurrence sequence from a kernel

DifferenceRoot symbolic representation of solutions to linear difference equations

### Sequence Recognition

FindSequenceFunction find formulas for sequences from data

### Sequence Visualization »

DiscretePlot plot 1D sequences given by formulas

DiscretePlot3D plot 2D sequences given by formulas

ListPlot, ListStepPlot plot sequences given as lists

### Sums & Differences

Sum () symbolic definite and indefinite sums, single and multiple ...

NSum numeric approximate sum

AsymptoticSum asymptotic approximate sum

DifferenceDelta () difference , inverse of sum

DifferenceQuotient difference quotients , approximate derivative

SumConvergence test for convergence of a sum

### Products & Ratios

Product () symbolic definite and indefinite products, single and multiple ...

NProduct numeric approximate product

AsymptoticProduct asymptotic approximate product

DiscreteRatio () ratio , inverse of product

### Difference Equations

symbolic solutions of recurrences and discrete functional equations

RecurrenceTable numeric solutions of recurrences

AsymptoticRSolveValue asymptotic solution of recurrences

### Sequence Limits

DiscreteLimit limits of sequences including recurrence and number theory

DiscreteMinLimit, DiscreteMaxLimit lower and upper limits

### Sequence Optimization »

Minimize find the global optimum of a sequence

### Other Sequence Operations

DiscreteShift shift ContinuedFractionK construct a continued fraction from a formula for terms