BUILT-IN MATHEMATICA SYMBOL

RecurrenceTable

RecurrenceTable[eqns, expr, {n, nmax}]
generates a list of values of expr for successive n based on solving the recurrence equations eqns.

RecurrenceTable[eqns, expr, nspec]
generates a list of values of expr over the range of n values specified by nspec.

RecurrenceTable[eqns, expr, {n1, ...}, {n2, ...}, ...]
generates an array of values of expr for successive , , ... .

Details and OptionsDetails and Options

• The eqns must be recurrence equations whose solutions over the range specified can be determined completely from the initial or boundary values given.
• The eqns can involve objects of the form where i is any fixed integer.
• The range specification nspec can have any of the forms used in Table.
• The following options can be given:
•  DependentVariables Automatic the list of all dependent variables Method Automatic method to use WorkingPrecision Automatic precision used in internal computations
• With , RecurrenceTable attempts to determine the dependent variables by analyzing the equations given.
• With , results for exact inputs are computed exactly, and for inexact inputs, the precision to use is determined adaptively at each iteration.
• With , a fixed precision p is used for all iterations.

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Solve an initial-value problem for a first-order difference equation:

 Out[1]=

Find the first few Fibonacci numbers:

 Out[1]=
 Out[2]=

Study the evolution for a nonlinear map of the plane:

 Out[1]//Short=
 Out[2]=

Compute a table of Stirling numbers of the first kind:

 Out[1]=
 Out[2]=