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RecurrenceTable

RecurrenceTable[eqns, expr, {n, n_max}]
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 n₁, n₂, ....

MORE INFORMATION

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 a[n+i] 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 DependentVariables->Automatic, RecurrenceTable attempts to determine the dependent variables by analyzing the equations given.

With WorkingPrecision->Automatic, results for exact inputs are computed exactly, and for inexact inputs, the precision to use is determined adaptively at each iteration.

With WorkingPrecision->p, a fixed precision p is used for all iterations.

Basic Examples (4)

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

Find the first few Fibonacci numbers:

Study the evolution for a nonlinear map of the plane:

Out[1]//Short=

Compute a table of Stirling numbers of the first kind:

Generalizations & Extensions (3)

Applications (6)

Properties & Relations (1)

Neat Examples (1)

RSolve Table FindInstance NDSolve

Demonstrations with RecurrenceTable (Wolfram Demonstrations Project)

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