This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
 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, Mathematica for the first time delivers a comprehensive system for discrete calculus. Symbolic Operations Sum, Product — definite and indefinite sums and products DifferenceDelta, DiscreteShift, DiscreteRatio — discrete differences and ratios 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 Generating Functions & Transforms GeneratingFunction — construct the generating function from the nth series coefficient SeriesCoefficient — find the nth term from a generating function 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      DiscretePlot — plot discrete sequences specified by formulas ListPlot — plot sequences given as lists Numerical Discrete Calculus MORE ABOUT Discrete Mathematics Number Theory Recurrence and Sum Functions Combinatorial Functions Integer Functions q Functions Continuous Calculus Discrete & Integer Data Image Filtering