# Questions tagged [recursion]

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

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### How to fix parameter locally for iterating recursion equations

The following is a simplified version of a more detailed problem. I have two coupled recursion equations of two variables, x and y. One equation also depends on a parameter, c: ...
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### Return[] in Recursive Functions [duplicate]

Here is the pseudocode I am using to demonstrate the problem. ...
1 vote
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### RecurrenceTable vs For loop : they do not give the same results. Why?

I have a second-order recurrence equation that I want to plot. I've used two different methods. The first uses RecurrenceTable, the second uses a traditional ...
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1 vote
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### Most efficient way of defining the following sets for every step $n$

For each $n\in\mathbb{N}$, how do we compute sets $A_n$ and $B_n$ below: Let $A_1=[0,2/3)$. Let $B_1=(2/3,1]$. If $A_n$ is a union of intervals, then for each interval cut out the middle $1/2^{n+1}$ ...
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### RSolve does not evaluate this recursion with two boundary conditions

I am using RSolve to solve for a function defined recursively, with two boundary conditions: First boundary condition describes the relationship between $f(1)$ and $f(0)$ Second boundary condition ...
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### Problem with RecurrenceTable of two variables

Let we have simple recursive function: ...
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1 vote
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### Strange errors of exceeding RecursionLimit in a function with two arguments, one set delayed and one fixed

INTRODUCTION Hi. I feel a bit embarrased asking this question as the answer may be staring me in the face and there are at least two other stackexchange articles related to it. MINIMAL WORKING EXAMPLE ...
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### Recursion limit for NDSolve

I have a fairly complex equation containing many terms, I can use the NDSolve for solving the differential equation for lesser terms (6400ish). But can't do it for ...
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### Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?

I have an ordinary differential equation and want to solve it using power series as ψ[x_] = Sum[Subscript[a, n] x^n, {n, 0, ∞}] to obtain the recurrence relation ...
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### Root finding for holomorphic functions, II

This is a follow-up to my question Root finding for holomorphic functions. I am trying to compute $10^6$ zeros of the derivative of the Riemann zeta function $\zeta(s)$ in the critical strip near ...
• 1,151
1 vote
56 views

### Solving a System of Recursively Defined Equations in Mathematica

I am trying to solve a system of equations in Mathematica where the variables are recursively defined. The system represents a probability distribution, and I want to find the values of the variables ...
180 views

### Finding the limit of a recursive sequence

I have come across a few different questions relating to my issue (namely this one, but the answers are not working for me. Here are my inputs; ...
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1 vote
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### How is my code going over the recursion limit?

I don't know how my code is exceeding the recursion limit of 1024. ...
79 views

### Recursion not working for higher terms

I am trying to find the terms x9,x10,x11 and y6,y7,y8 and so on from the recursive relation given in the code. ...
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1 vote
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### Sorting a list of functions by exploiting the recursive structure

Given a list of functions list and a vector of arguments {t, a}: ...
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### Symbolic recursion

I have the two recursive relations: ...
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### Calculate Bernoulli numbers ( with a twist) [closed]

Mathematica has an inbuilt function BernoulliB that calculates $B_n$ for which, $$\frac{t} {\left(e^t-1\right)}=\sum_{n=0}^{\infty} \frac{B_n}{n !}t^n$$ I need to ...
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1 vote
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### Understanding HoldFirst in QuickSort algorithm

I have read the implementation of QuickSort algorithm in WL from Roman Maeder's Computer Science with Mathematica (2000). The implementation is shown below. ...
128 views

### Recurrence formula evaluating with speacial counting of subscripts

Hoping to check some recurrance relationship like this $a_1 = x$ and $a_2 = y$, with $$a_{2n+1} = a_{2n} a_{2n-1}$$ and $$a_{2n+2} = a_{2n+1} + 4$$ Tried ...
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### Optimization of a Markov сhain with symbolic transition rate

I am trying to work on 1D random walk that can move to left, right or stay with probabilities $p_i$,$q_i$,$r_i$ that changes with the site $i$. I am trying to simulate this by using a recurrence ...
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1 vote
163 views

### How do you Solve a Simultaneous System of Recursions

Consider the following system of simultaneous recursions: r[n] == s[n-1] s[n-2] == r[n-3] I am tring to solve this system (I have given a vastly simplified ...
1 vote
86 views

### Recursively applying a substitution

I have an expression like this: 2v[j-1]-(s[j]+1)(c[j]-c[j-1]) >= v[j] I want to apply this recursively say k times. I can do one step like this: ...
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1 vote
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### SummaryBox and Recursion

How can I make it so that what is under the dropdown block is not calculated/constructed at once? Example code: ...
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### Recursive function with subscript

I am trying to define a recursive function with a subscript. Something similar would be $f_{n+1}(x) = \int 3 x f_{n}(x)dx$. I've tried lists, For function, ...
1 vote
90 views

### A recursion in a sum [closed]

I wish to use a recursion to continue the updating n2, n3, etc., up to n30. Probably simple concept for an experienced MM user. Sorry. ...
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### Use two derivative rules and iterate several times to get the simplest expression of higher derivative

I have 2 rules of recursive relation of the derivative, I want to use it several times get the higher derivative on [\Theta] of ...
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### Recurrent equation with UnitStep function using RSolve

I have the following equation to solve $$a[n+1] = a[n] + 6 - 100\cdot \theta(a[n]-100)$$ where $\theta(x)$ is the Heaviside step function. So I tried the following ...
135 views

### Kernel crashes after long iterations

I am trying to get a numerical root of a function defined as below. But after some large recursion the kernel get crashed. But for relatively low recursion(10000) that does not make any problem. But I ...
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1 vote
106 views

### Module returning Null even with Module as a Return parameter

I'm currently trying to implement Newton's method of approximating roots to approximate the root of 2. I looked into some possible reasons as to why it would return Null, such as the scope of the ...
900 views

### V 13.2 gives TerminatedEvaluation["RecursionLimit"] on code which works before. Why?

Update June 25, 2023. Problem still there in V 13.3. Added screen shot at end. I was trying code which worked all the time: How to extend a function by period and display it I find that in V 13.2 it ...
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### Problem with For Loop when evaluating a recursive function at multiple points

I am running into problems with my For loop when trying to evaluate my expression. Fix some parameter values : ...
449 views

### Plastic number rectangle

I'd like to find a nice recursive way of making this image based on the plastic constant Here's a start ...
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### Recursive function Catalan triangle

I'm trying to learn how to build a recursive function. However, I'm not sure to understand how to set a "limit". Here is what I'm trying to make. I want a function that gives me the i,j ...
1 vote
141 views

### Speed up calculation of recursively defined list

I have two lists $a$ and $b$ of length $n$ and $n-1$ respectively (typically I have $n \approx 1000$). I have to compute a list $\theta$ of length $n$ which is defined recursively by the following ...
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