LinearRecurrence
LinearRecurrence[ker,init,n]
gives the sequence of length n obtained by iterating the linear recurrence with kernel ker starting with initial values init.
LinearRecurrence[ker,init,{n}]
gives the n term.
LinearRecurrence[ker,init,{nmin,nmax}]
yields terms nmin through nmax.
Details
- The ker and init can involve arbitrary symbolic expressions, as well as arrays.
- The initial list init must be at least as long as the kernel list ker.
- If init is longer than ker, only the last Length[ker] elements are used.
- LinearRecurrence[{a1,…,ad},{y1,…,yd},n] iterates the recurrence equation with initial conditions , …, .
- When coefficients ai and initial values yj are arrays, then the iterated recurrence is interpreted as with dot products of values and the reversed coefficients.
- If the initial values yj have dimensions {m1,…,ms} then the coefficients ai must either be scalar or must have dimensions {m1,m1}.
Examples
open allclose allBasic Examples (3)
Scope (2)
LinearRecurrence works with symbolic kernels and initial values:
LinearRecurrence works with arrays:
Generalizations & Extensions (2)
Applications (2)
Properties & Relations (1)
RSolve finds a symbolic solution for difference equations:
LinearRecurrence generates a procedural solution:
Obtain the same result using RSolveValue:
Neat Examples (1)
Text
Wolfram Research (2008), LinearRecurrence, Wolfram Language function, https://reference.wolfram.com/language/ref/LinearRecurrence.html (updated 2017).
CMS
Wolfram Language. 2008. "LinearRecurrence." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/LinearRecurrence.html.
APA
Wolfram Language. (2008). LinearRecurrence. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LinearRecurrence.html