# Discrete Calculus

With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. Building on a large body of original research at Wolfram Research, the Wolfram Language for the first time delivers a comprehensive system for discrete calculus.

### Symbolic Operations

Sum, Product definite and indefinite sums and products

DiscreteShift shift DifferenceDelta difference DiscreteRatio ratio etc

DifferenceQuotient difference quotients etc.

SumConvergence test for convergence of a sum

ContinuedFractionK construct a continued fraction from a formula for terms

### Difference Equations

RSolve symbolic solutions of recurrences and discrete functional equations

RecurrenceTable tables of values from recurrences and functional equations

RSolveValue find an expression for the solution of a difference equation

### Sequence Limits

DiscreteLimit limits of sequences including recurrence and number theory

DiscreteMinLimit, DiscreteMaxLimit lower and upper limits

### Special Sequences »

LinearRecurrence generate a linear recurrence sequence from a kernel

DifferenceRoot symbolic representation of solutions to linear difference equations

### Asymptotics »

AsymptoticSum asymptotic approximation to sum

AsymptoticRSolveValue asymptotic approximation to difference equations

### Sequence Recognition

FindSequenceFunction try to find functional forms for sequences

### Continuous Calculus »

Integrate definite and indefinite integrals

### Sequence Visualization »

DiscretePlot plot discrete sequences specified by formulas

DiscretePlot3D plot 2D discrete sequences

ListPlot, ListStepPlot plot sequences given as lists