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.
Sum,
Product — definite and indefinite sums and products
SumConvergence — test for convergence of a sum
ContinuedFractionK — construct a continued fraction from a formula for terms
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
n
series coefficient
SeriesCoefficient — find the
n
term from a generating function
LinearRecurrence — generate a linear recurrence sequence from a kernel
DifferenceRoot — symbolic representation of solutions to linear difference equations
FindSequenceFunction — try to find functional forms for sequences
DiscretePlot — plot discrete sequences specified by formulas
ListPlot — plot sequences given as lists
Numerical Discrete Calculus
