# recurrence

1. ### non-homogeneous recurrence problem

Hello everyone, I have this problem $a_n + a_{n-1} + 6a_{n-2} = 5n(-1)^n + 2^n$ This is the given solution: a_n = (\sqrt{6})^n(C_1\cdot \sin\phi n + C_2\cdot \cos\phi n) + \frac{1}{3} \cdot 2^n + \left(\frac{5}{6}\cdot n + \frac{55}{36}\right)(-1)^n I used the discriminant to find the zeros...
2. ### An equation of recurrence

Hello all, Solve the recurrence equation f''(x-2)+f''(x)+f''(x+2)=2f''(x+1). All the best, Integrator
3. ### Recurrence relation

For second order linear homogeneous recurrence relation with constant coefficients, is it that the general sequence is only in the form of 1, t, t^2, t^3, ..., t^n or just one of the general sequences which satisfies the characteristic equation? Thank you.
4. ### Solving recurrence of order n

Hi, I came across this sequence $u_n$ where $u_1=1$ and subsequent terms are given by the recursive formula $$u_{n}-\sum_{k=1}^{n-1}T(n,k)u_{k}=f(n)$$ where $T(n,k)$ are real non constant coefficients and $f$ is a given function. Is there a general method to solve this equation? ... Thanks...
5. ### A recurrence equation

Hello everybody, Solve the recurrence equation |f(x^2+1)-f(x^2-1)|=3x^2+2x+1. All the best, Integrator
6. ### recurrence formula problem

how to solve it? a0=a1=1 thank you!!
7. ### How to find order of a recurrence relation? help

Hi, I'm in a hurry, for example : an= an-1 + an^2-2 there order of this function is "2" how is that be? and what is the meaning of order please help me,
8. ### Question regarding Particular solution in recurrence relation

Hey all, I need help with solving a recurrence relation using homogeneous+particular function. * I have no issue finding the homogeneous coefficients, I only need help with the particular (non-homogeneous addition) f(n) = 5f(n-1)-6(n-2)+n \cdot 2^{n-1} \\ Homogenous\, roots: (x-2)(x-3)...
9. ### Recurrence Sequence

The non-zero values for $x_0$ and $x_1$ such that the sequence defined by the recurrence relation $x_{n+2} = 2x_n$, is convergent are A) $x_0 = 1$ and $x_1 = 1$ B) x_0 = \frac{1}{2} and x_1 = \frac{1}{4} C) x_0 = \frac{1}{10} and x_1 = \frac{1}{20} D) none of the above I have checked the...
10. ### recurrence relation problem

Hi, I would like to get help with the following recurrence relation problem. Thanks in advance.
11. ### Solve this recurrence relation with repeated subsitution

\sqrt(n)T(\sqrt(n)+n I've tried what I think is right, but I came up with: (n^{1/2}*n^{1/2^{2}}*...*n^{1/2^{k}})T(n^{1/2^{k}})+(n^{1/2^{k-1}}+...+n^{1/2}+n) And I have no idea how to find the pattern of that so I'm hoping I'm wrong.
12. ### Help solving simple Recurrence Relation.

Hello, I'm not a mathematician, but a physicist, so I have no idea how to solve those recurrence relations, but I need to solve one (it's related to a closure phase calculation in optical interferometry). First of all I have the following recurrence relation: G(n \Delta x)=\phi[(n+1)...
13. ### Non-linear Recurrence Equations

Good morning, Please to provide me with any book that discusses and explains all the methods for solving non-linear equations in detail. Thanks a lot.
14. ### Solve this Recurrence Relation?

Can Anyone provide a function satisfying: f(1) = 1 f(x) = 1 + x/f(x) This isn't homework or anything, just something I stumbled across.

16. ### Recurrence equation

Hello! Solve the recurrence equation a'_{n}-a_{n-1}+n^2-2n=0.
17. ### Discrete Mathematics: Linear homogeneous recurrence of order 2

Well i've learned the solution of solving linear homogeneous recurrence equations of the second order from the book "discrete and combinatorial mathematics" of Ralph Grimaldi. But there was just an unclear tutorial of the solution with no explanation on how this solution is made, what's its...
18. ### Recurrence sequence - proof

Hey, can you help me with this problem? :) Let m be positive integer and let's define a recurrence sequence: a(0)=a(1)=1, a(n+2)=a(n+1)+a(n)*e^(2Ï€i*(n+1)/m). Prove that: a(2m)=a(m)+1
19. ### Recurrence

Hello all! I have some problem in figuring out how to solve the recurrence a_n = 2 a_{n-1} sqrt{1-a_{n-1}^2} for n > 0 with a_0 = \frac{1}{2} and with a_0 = \frac{1}{3} . In particular, what I want to ask, is some good transformation in order to change variables. Trying b_n = n a_n or b_n =...
20. ### recurrence relations

Hello, will someone please help me figure out how to if an+1=sqrt(2+an) Show that for all n âˆˆ N we have an+1 - an =(an- an-1)/(sqrt(2+an)+sqrt(2+an-1))