Tagged Questions

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

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1
vote
1answer
74 views

Limit as n -> ∞ for RSolve with Multivariate Recurrence Relation

I'm trying to solve the following when n -> ∞: ...
1
vote
0answers
20 views

Solving a pair of recurrence relations [duplicate]

Why does this RSolve[{y[t] == a*y[t - 1]}, {y[t]}, t] work, while this ...
0
votes
1answer
107 views

How to plot particular piecewise defined functions in mathematica

How to plot such functions in Mathematica? Let $a_0, p,g,c$ be any positive integers, defining: $$a_{n+1} = \begin{cases}\frac{a_n}{p} &, a_n \text{ divisible by p}\\ ga_n +c &, a_n \text{ ...
0
votes
0answers
264 views

Caching RecursionLimit::reclim error

I am learning how to catch exceptions, RecursionLimit::reclim in particular. To see how it works, I came up with the following example: ...
4
votes
1answer
203 views

Creating a dynamic plot directly from the recurrence relation

I have the following recurrence relation that has no general solution: $$x(t+1) = \frac{x^2 + x(1-x)(1-sh)}{x^2 + 2x(1-x)(1-sh) + (1-x)^2(1-s)}$$ In Mathematica language it gives: ...
2
votes
0answers
147 views

Faster Ways to compute recursive summation

It takes a long time to compute the summation below, and I'd like to know if there are some better ways to compute things faster. I have used $3$ ways to calculate, but they are very unsatisfactory. I ...
6
votes
3answers
264 views

Nested list to graph

The following nested list can be regarded as a representation of a (tree) graph: ...
0
votes
1answer
77 views

How to define a function that operate with a base case recursively? [duplicate]

Let's start from the simplest case: say I have a function $f(x)=x$, and let's say I want to define a new function (of $x$) to be its $n$-th power $(f(x))^n$. How should I write the code? I tried: ...
1
vote
2answers
151 views

Summing Over a Variable Number of Indices

I am trying to figure out the best way to include a variable number of indexes of summation in a program. For example: Suppose I want to define a function $g[n,s]$ that returns the sum ...
2
votes
2answers
157 views

Solving a dynamic program via recursion

I'm trying to use recursion to solve a joint inventory/ dynamic pricing problem as in monahan, petruzzi and zhao 2004. I tried to solve for y[t] and ...
3
votes
2answers
136 views

Unset while running recursion

I am trying to run a recursive definition while at the same time clearing previously found values, so my memory is not completely consumed. I found this: How to clear parts of a memoized function? ...
6
votes
1answer
299 views

What is the most elegant way to specifiy a start case for recursion?

When writing recursive code that computes the least value at which a condition is true and various other scenarios it is often necessary to specify a base case. What I have done to supply this is ...
0
votes
1answer
81 views

Defining a formal Primitive Recursion

I'm searching for a way to define the function this wikipedia article call Primitive Recursion. It should have two functions as argument and it should return a function. I need this as helping in ...
1
vote
1answer
138 views

Defining a recursive integral sequence

I have a recursive integral sequence as follows: $$y_0(x)=1+r,$$ $$y_1(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_0(t) dt,$$ $$\vdots$$ $$y_n(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_{n-1}(t) ...
0
votes
1answer
104 views

How to solve the recursion equation that include the uncertain value i in it?

I write the following code of a recursion equation, but it can not work correctly. ...
2
votes
1answer
211 views

calculating a sequence of functions using iteration

I am trying to compute a sequence of functions using iteration and keep running into problems trying to use built in looping commands because of the recursive nature of the definition. The code below ...
11
votes
7answers
388 views

Concatenation of lists in a Fibonacci-like pattern

I am trying to create a List of elements that follow the general pattern: $$X_{n+1} = X_n X_{n-1}$$ where the operation on the right hand side is concatenation, i.e., joining. I want to achieve the ...
0
votes
1answer
114 views

Explicit, closed formula for recursive integral as a function of the recursive parameter

This is a follow-up of this question/answer. I'm working on a recursive integral more complicated than the one on the linked question, but this one can be used as an example. I would like to obtain ...
4
votes
1answer
213 views

Computing a series in terms of exponential function

Is there any way to compute the following series in terms of exponential function ? $$\sum_{k=0}^\infty Y_1(k)\;x^k$$ where $$Y_1(k) = \frac{(k - 1)!}{k!}Y_3(k - 1)$$ $$Y_2(k) = \frac{(k - ...
1
vote
1answer
611 views

Why do I get an error message when for this type of recursion?

When I type the following code: mus[] = 0; mus[x__] := First[List[x]] + mus[Rest[List[x]]] What one would think would happen is that if, ...
1
vote
1answer
441 views

Solving a nonlinear system of recurrence equations

I am having two problems regarding Mathematica, and both of them are happening because it does not accept such inputs: ...
5
votes
1answer
150 views

How can I use a recursive function in a Module

I have a question about using a recursive function in a module. I made the following example to illustrate the question. The followwing code works: ...
5
votes
3answers
412 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 ...
5
votes
1answer
218 views

How to deal with too much recursion

I have put together a very simple climate model based around four equations which define the state at time t based on time t-1, ...
3
votes
2answers
149 views

Rook walk and RecurrenceTable in Mathematica

This appears in a combinatorics book: $a(m,n)=2 a(m,n-1)+2 a(m-1,n)-3 a(m-1,n-1)$ It is a recurrence equation for the number of rook walks from $(0,0)$ to $(m,n)$. The initial conditions are: $ ...
2
votes
2answers
71 views

Optimize recurrence output

I have recurrence and I need to calculate first $N$ members of the sequence ...
9
votes
2answers
316 views

Recursive Integral for Volume of $n$-Ball

The volume of an $n$-ball (the $(n+1)$-dimensional analogue of a disk) of radius $r$ can be found by the following integral recurrence: $$V_0(r)=2r$$ ...
3
votes
4answers
429 views

Recursive function for calculating the arithmetic mean of a vector

I want to write recursive function for calculating the arithmetic mean of a vector. For $X(n)=\{1,2,3,\ldots, n\}$, the formula is ${\rm Mean}(X(n))=((n-1)\, {\rm Mean}((X(n-1))+X_n)/n$. My ...
4
votes
3answers
170 views

Long waiting time for computing a summation

It takes a long time to compute the summation below, and I'd like to know if there are alternative ways to compute things faster. When replacing $15$ by $\infty$, then I should get $3^{1/3}$. I need ...
2
votes
2answers
313 views

Recursive formula involving a piecewise function

I am trying to construct a recursion, g[t], where g[t] = a[t] if g[t-1] = 1 ...
8
votes
1answer
281 views

How can I define a Listable function only apply to a vector?

Consider the function f which should behave as f[{{1, 2}, {3, 4}, {5, 6, 7}}] ...
8
votes
3answers
423 views

Create sine function with random increase in phase

I am trying to simulate a signal that randomly increases its phase, so far I have tried two thing but neither worked. I usually use matlab but I want to learn some Mathematica so I thought I would try ...
0
votes
1answer
131 views

fit recursive function to data

I have a function $g(x, n)$, which is a recursive expression: $x$ is a variable and $n$ the number of iterations. In my case $n=3$ for all $x$. An example is the following: ...
2
votes
1answer
143 views

Integral of GeneratingFunction

I know that GeneratingFunction can be used to compute the generating function $\sum_{n=0}^\infty a_n x^n$ of a sequence $(a_n)_n$ via GeneratingFunction[a[n],n,x] ...
7
votes
0answers
261 views

Compile recursive function modifying global variables

How to compile recursive formula when it relies on more than a few global variables (global to the topmost compiled function)? It is unreasonable to pass on all such variables to each recursive ...
3
votes
1answer
287 views

Transform recursion for coefficients into differential equation for generating function

Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as a[i] == i a[i-1] I would like to convert this recursion ...
7
votes
2answers
356 views

How can I define a sequence of functions?

I need to define a function fun, and then re-define this function iteratively. The code is given at the end. First, a function ...
1
vote
1answer
249 views

How can I solve my recursion equation?

How can I solve the recursion equation given below? I doubt there have no solution for the recursion equation because this is circulating recucrsion equation. ...
3
votes
1answer
183 views

Converting this recursive function definition into nested sums?

Here's the recursive function I'm using: DH[n_, k_, s_] := Sum[Binomial[k, k - j] DH[n/m^j, k - j, m + 1], {m, s, n^(1/k)}, {j, 1, k}] DH[n_, 0, s_] := 1 Now, ...
7
votes
1answer
144 views

Recurrences of lists

Assume we have a multi-dimensional recurrence, e.g. $\qquad\begin{align*} a_1 &= (1,2) \\ a_n &= (1,2) + a_{n-1} \quad, n>1 \end{align*}$ with the easy solution $a_n = (n,2n)$. How ...
3
votes
2answers
192 views

Implementation of a recurrence relation for the polynomials appearing in the large order asymptotics of the Bessel functions

I would like to implement the recurrence relation for the polynomials $U_n(x)$ appearing in the large order asymptotics of the Bessel functions. The recurrence in question is ...
1
vote
4answers
368 views

Recurrence relation in a table

I am trying to generate a list of x-values for a function using a module, where my x-value must increase by 'a' if the term ...
4
votes
0answers
119 views

Efficient Generation of Subgraphs (or, unfriend a friend a day)

NB: If you're not interested in the back-story, you could simply jump forward to the code which I'm seeking to optimize. Also, I believe this code would only work for MMA 8.0 and above. My friends ...
0
votes
0answers
30 views

Keeping memory to reduce the running time of recursion [duplicate]

I am using the following recursion in Mathematica to compute W[n, 1, s] for given n and s: ...
8
votes
5answers
280 views

Wrapping a function in count

I am working through the Programming Paradigms via Mathematica (A First Course) and am attempting to answer the following: Use recursion to count how many times the argument can have its square ...
8
votes
4answers
404 views

Partitioning a list by recursion (Programming Paradigms via Mathematica (A First Course))

I am working through the course Programming Paradigms via Mathematica. One of the homework exercises for the section Recursion I: Passing the Buck is as follows: Use recursion to partition a ...
1
vote
2answers
98 views

Using RecurrenceTable index to call elements of a vector

I am having trouble doing something that seems straightforward. I have a recursive sequence that I would like to produce which looks as follows: ...
1
vote
1answer
147 views

Recursive function taking functions as arguments

I'm trying to implement Lie brackets and derivatives of nth order. For doing this, I've stumbled upon something I don't understand. Here is an illustration: First I define the functions: ...
2
votes
1answer
491 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
4
votes
3answers
185 views

Modify this code using Module and While

I have written a recursive function and would like to re-write the code using Module AND While to compare the timings. Here is my recursive function for f[n], where 6 n f[n] = f[n-1] + n! for n>0 and ...