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

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4
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1answer
460 views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
4
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1answer
296 views

Error Interpretation in NIntegrate

I am using a recursion algorithm developed by Migdal for Lattice Field Theory, and I have the following code: ...
4
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0answers
110 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 ...
3
votes
2answers
124 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? ...
3
votes
2answers
161 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 ...
3
votes
4answers
304 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 ...
3
votes
1answer
154 views

How to make a simple tree yourself with defined distances for each generation?

I'm trying to make a function that generates a tree for spin spin analysis in spectroscopy. I though it would be pretty easy, but I'm totally stocked. The tree should look something like this: ...
3
votes
1answer
168 views

How do I built a zoomable Koch curve?

I'm new to Mathematica and my goal is to write a simple program in order to demonstrate self-similarity of the Koch curve by zooming in. Here is a good example of what I mean (it's a Java applet). I ...
3
votes
1answer
331 views

How to implement Condition programmatically?

I am writing my own symbolic functions with custom symbolic properties. So often I wish to introduce some automatic simplifications or evaluations, which return the same head as it's argument. This ...
3
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1answer
66 views

Find exact limit of recurrence relation $x_{n+1}=\cos(x_n)+1, x_0=1$

I did this: b[x_] := Cos[b[x - 1]] + 1; b[0] = 1; num = SequenceLimit[N[Table[b[n], {n, 1, 100}], 50]] I also did the listplot which shows a convergent value. ...
3
votes
1answer
158 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it ...
3
votes
1answer
116 views

Using NestWhileList to determine smallest prime value in series

I have a function recursively defined as follows: $a_{n+1}-1=(a_n-1)\times lpf(a_n)$, whe $lpf(x)$ is the least prime factor of $x$. Now, given an initial value of $a_0$, I would like to find the ...
3
votes
1answer
200 views

Avoid crash in recursive Dynamic

With the following Dynamic cell, I can reproducibly crash Mathematica, so do not try this unless you have saved all your work! ...
3
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1answer
158 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, ...
3
votes
1answer
737 views

Solve pair of recurrence relations

[Corrected equations and added simple example] Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow? ...
3
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0answers
228 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 ...
3
votes
0answers
280 views

Solving recursion relations using Mathematica

I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
3
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0answers
92 views

An recurrence equation that can be solved in version 7 but not in version 8

A friend of mine showed me this code sample: RSolve[{a[n] == a[n - 5] + 1, Sequence @@ Table[a[i] == 1, {i, 5}]}, a[n], n] // Timing It's solved by version 7 in ...
2
votes
3answers
542 views

Recursive function on list

Please consider the following: I have to deliver the weekly customer demand data on time. I can start to produce my products one week in advance. So I was thinking ...
2
votes
2answers
97 views

Rising Recursion Relationships

Lets say I want to compute the following function in mathematica: $G[n,k]=G[n+1,k-1] + G[n+2,k-2]$ where I know that $G[n,0]=n$ and $G[n,1]=n^2$. So, for example, $G[3,2]=G[4,1]+G[5,0]=4^2+5$ or, ...
2
votes
2answers
561 views

defining recursively a function with multiple if conditions

I am trying to recursively define a function which satisfies the following system of equations and which depends on two parameters $n$ and $l$, $$ \begin{align} A(x, n, l) &= F[ A(x,n-1,l) ]\\ ...
2
votes
2answers
117 views

Recursion doesn't happen any more or doesn't happen correctly if I store the recursive relationship in a variable first

I know the following code will form a recursion: Clear["Global`*"] u[i_, n_] := u[i - 1, n] + u[i, n - 1] u[0, n_] := n u[i_, 0] := i u[2, 2] (* => 8 *) But ...
2
votes
2answers
725 views

How to define functions for a parameter-dependent recursive sequence

I am trying to generate a two variable recursive sequence For instance on Mathematica, I did z[1] := {1, 1} B := {{t, 1}, {-1, t}} z[n_, t_] := B.z[n - 1, t] ...
2
votes
1answer
172 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 ...
2
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1answer
95 views

Notation not recursive enough?

My notation is not recursing enough. For example, Notation[W[a_ | b_] ⟹ foo[a_, b_]/foo[b_]] Notation[W[a__, b_ | c_] ⟹ W[a__ | c_]W[b_ | c_]] Then ...
2
votes
2answers
254 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 ...
2
votes
1answer
356 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
2
votes
1answer
137 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] ...
2
votes
2answers
139 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 ...
2
votes
2answers
134 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
0answers
114 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 ...
2
votes
0answers
85 views

RSolve and incomplete gamma function

I am interested in how Mathematica uses the incomplete gamma function to solve difference equations. For example, if we have this inhomogeneous, 2nd order equation and use ...
2
votes
0answers
186 views

Nonlinear recurrence relation

I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{n−1})^3)} 3$$ Is there another way to get a formula for the nth term?
2
votes
0answers
180 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. ...
1
vote
1answer
153 views

Differentiation w/o assiging concrete values

v = Subscript[v, 0]*Sin[(Pi*S)/Subscript[S, 0]]; a = dv/ds v; a = D[v, s] returns ...
1
vote
4answers
315 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 ...
1
vote
1answer
2k views

Defining a recursive sequence

I want to define a recursive sequence and then ask Mathematica to print a specific value: Am I doing something wrong?
1
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3answers
248 views

List of Tribonacci Polynomials with Mathematica? [duplicate]

I want to list top ten of Tribonacci polynomials. I have following algorithm, but it doesnt work. ...
1
vote
1answer
240 views

Finding n-th term of a sequence of functions

Lets say, I have the following series of functions, $f_1=a+1$ $f_2=a^2+2a+1$ $f_3=a^3+3a^2+3a+1$ Assume that $f_4, f_5,$ and $f_6$ are also known. However $f_n$ is not known as a function of $n$. ...
1
vote
1answer
167 views

Using different random values at each recursion step

I have the following code: ϕ[0] := π/4 ϕ[n_] := Exp[-n] ϕ[n - 1] + Sqrt[1 - Exp[-2 n]] M M = RandomVariate[NormalDistribution[0, 1]] For this recursion relation, ...
1
vote
2answers
67 views

Optimize recurrence output

I have recurrence and I need to calculate first $N$ members of the sequence ...
1
vote
2answers
211 views

While-Loop Linear Projection

I'm would like to do a linear progression for a recursive relation of a consumption function. Combining my program skills and my sparse knowledge of mathematica, I was thinking about doing it in a ...
1
vote
2answers
116 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 ...
1
vote
1answer
121 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) ...
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2answers
43 views

Print argument of function that exceeds $RecursionLimit

Is there a way to print the argument of a function which results in a $RecursionLimit::reclim error? As an example, cosider the code ...
1
vote
1answer
57 views

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

I'm trying to solve the following when n -> ∞: ...
1
vote
1answer
220 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. ...
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2answers
96 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
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1answer
129 views

Unwanted hold in recursive function

I have a function (let it be called f) that does something useful for me and I want to be able to apply it to the elements of a list regardless of their depth and keep the list structure. For example ...
1
vote
1answer
148 views

Recursion evaluate Table power exceeded limit

I wrote 2 simple recursive functions for calculating the power of a table. pol3[Tb_List, n_Integer?Positive] := If[n == 1, Tb, Tb.pol3[Tb, n - 1]] and ...