What is Recurrence: Definition and 256 Discussions
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given; each further term of the sequence or array is defined as a function of the preceding terms.
The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation. However, "difference equation" is frequently used to refer to any recurrence relation.
For our combinatorics class there is a bonus excercise in which we have to solve the following recurrence relation:
L_k(x) = L_{k-1}(x) + xL_{k-2}(x)
My first thought was to construct the following generating function:
F(x,y) = \sum_{k=0}^{\infty} L_k(x) y^k.
By putting in the...
A set of blocks contains blocks of heights 1, 2, and 4 inches. Imagine constructing towers of piling block of different heights directly on top of one another. Let t(n) be the number of ways to construct a tower of height n inches. Find a recurrence relation for t(1), t(2), t(3)...
Here's...
Hi...
1. so can i say that a recurrence relation is a description of the operation(s) involved in a sequence...?...
2. is the formula for an arithmetic sequence, a recurrence relation...?...
and is the formula for a geometric sequence,
a recurrence relation...?...
I need to show that the solution of
a_n = c_1a_{n-1} + c_2a_{n-2} + f(n) (1)
is of the form
U_n = V_n + g(n) (2)
where V_n is the solution of a 2. order linear homogenous recurrence relation with constant coefficients.
Could I use the argument that if (2) is a solution...
Lectori salutem.
Can anyone refute the finite space/energy/matter in infinite time theory?
Finite space/energy/matter implies that the universe is not something endlessly extended, but set in a definite space as a definite force.
Infinite time implies that it has never begun to become...
Lectori salutem.
This seems like a cosmological question, so I will put it here:
Can anyone refute the finite space/energy/matter in infinite time theory?
Thanks in advance.
Sauw