# Questions tagged [difference-equations]

Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.

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### Solving partial recurrence equation with several recurrence indices

I'm trying to solve a recurrence relation for a function of three variables. It works with 2 variables but not with 3. A simple example is: ...
263 views

### Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
54 views

### Avoid Recursion in lag and difference operations

I have a panel data situation and I'm interested in taking lags and differences and using Mathematica to simplify the algebra of the result. Currently I'm working with a model like this: ...
74 views

### Solving recurrence equation with variable $x$

Please I want to solve this recurrence equation $$p_n(x)=\frac{1}{x}\left[\frac{n\;}{\sqrt{2 n-1} \sqrt{2 n+1}}p_{n-1}(x)+\frac{(n+1)}{\sqrt{2 n+1} \sqrt{2 n+3}}p_{n+1}(x)\right]$$ $x$ is a variable ...
36 views

### How to specify an element of a list when using RecurrenceTable

My problem is that I'm trying to get a list of refraction angles in a multilayer structure (for the sake of this example - with two types of refraction indices and eleven layers of them). The code is ...
409 views

### Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
55 views

### Computing a system of ordinary differential equations with initial condictions over a continuous range [closed]

I have some questions about Mathematica programming and would appreciate if you could help me. I want to solve a system of ordinary differential equations μ '[t] ...
58 views

### What is the fastest way to calculate series from recurrence solutions with no closed form?

I am not very experienced with Mathematica. I want to calculate the series from recurrence solutions. These solutions have no closed-form. I want to improve the approximation and hence need a good ...
60 views

### recurrence equation

The output of Mathematica is only a copy of the input. What am I doing wrong? ...
21 views

### Does Mathematica find most general recurrence solutions?

Consider e.g. the following recurrence relation solution: RSolve[a[m, n + 1] == a[m + 1, n], a[m, n], {m, n}] {{a[m, n] -> C[m + n]}} which states that the ...
31 views

### Problems with the parametric Recurrence Table

I am trying to construct a minimization program where I have to minimize a function with respect to a matrix. This matrix enters into the optimization program in a convoluted manner together with data....
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### How do I use RSolve to solve the problem below?

RSolve can't compute the solution. Appears that Mathematica is having a convergence problem. I don't know if the boundary conditions are properly defined... ...
36 views

### Residues of products

i have the following problem: My function is given by: $(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$, ...
Please I am struggling to compute with mathematica the first 5th iterations of the sequence of functions $u[n,t]$ satisfying the integro-differential equation Please help me with the code. Patrick