# Tagged Questions

For questions about defining recursive functions, recursive algorithms and solving recursive equations.

293 views

### Calculating N-th step of recurrent sequence

I am figuring out how to calculate the $n$-th step of a square root approximation sequence: $$x_{n+1} = \frac12\left(x_{n} + \frac{a}{x_n}\right),$$ where $a$ is a number the root of which is to be ...
656 views

### How does one clear the memory of a recursive function

I want to implement the recursive function v[n_] := v[n] = v[n-1] + f[n-1] + Random[NormalDistribution[0,s]] to get ...
281 views

### Iterating a rational function

I'm reading about iterating rational functions. I'm given $$R(z)=\frac{3z-2}{2z-1},$$ then the author makes the statement: "Then(by induction), $$R^n(z)=\frac{(2n+1)z-2n}{2nz-(2n-1)}.$$ Is there a ...
244 views

507 views

### Plotting two recursive functions

I'm trying to plot two recursive functions (p and θ) on a map. So far I have: ...
205 views

### How can I make a “self-referential” replacement operation self-contained?

Fairly often I find use for replacement rules that call themselves on the right-hand side of the rule, e.g.: ...
157 views

### RSolve gives a Context::ssle error

Bug introduced in 9.0 or earlier and fixed in 10.0 I want to solve the following recurrence equation RSolve[{(k + 2) c[k + 2] q^(k + 1) - c[k] == 0}, c[k], k] ...
301 views

### Can the general term my recurrence equations be written with Floor or Mod?

I want to know the formula for the general term of the following recurrence system. I guess it can be written with Floor or Mod. ...
85 views

### Solution to Simultaneous Arithmetic/Geometric Mean Recursion Relations

I'm trying to solve the simultaneous convergent sequences of geometric/arithmetic means where $a_{n+1}=\frac{1}{2}(a_n+b_n)$ and $b_{n+1}=\sqrt{a_nb_n}$ and initial values are $a_0=1+x$ and $b_0=1-x$. ...
464 views

### Solving recurrence sequence using an ODE

I'm trying to solve the recurrence a[n] == 0 for n < l a[l] == 1 a[n] == (l + 2(n - l) a[n - l] + (n - l)(n - 1) a[n - 1])/n(n - l + 1) for n >= l using ...