# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
WOLFRAM LANGUAGE GUIDE

# 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.

## ReferenceReference

### 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

### Generating Functions & Transforms

GeneratingFunction construct the generating function from the n series coefficient

SeriesCoefficient find the n term from a generating function

### Special Sequences »

LinearRecurrence generate a linear recurrence sequence from a kernel

DifferenceRoot symbolic representation of solutions to linear difference equations

### Sequence Recognition

FindSequenceFunction try to find functional forms for sequences

### Sequence Visualization »

DiscretePlot plot discrete sequences specified by formulas

DiscretePlot3D plot 2D discrete sequences

plot sequences given as lists