Questions tagged [recursion]
For questions about defining recursive functions, recursive algorithms and solving recursive equations.
659
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How to Set Precision for an RSOLVE Problem
The following code was working fine -- now it produces errors. I originally built this in ver 13.1 and I'm now running ver 14. I think I'm getting machine precision errors after k=11 that were not ...
- 1,773
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3
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85
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2
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2
answers
46
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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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0
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57
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Return[] in Recursive Functions [duplicate]
Here is the pseudocode I am using to demonstrate the problem.
...
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1
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2
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118
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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
answer
89
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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 $1/2^{n+1}$ ...
- 81
3
votes
2
answers
61
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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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2
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1
answer
86
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1
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1
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41
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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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63
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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 ...
- 21
3
votes
2
answers
222
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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 ...
- 63
2
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1
answer
74
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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 ...
- 1,161
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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 ...
2
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3
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188
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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
answer
108
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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.
...
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1
answer
79
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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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2
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180
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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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2
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137
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0
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3
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112
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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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0
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74
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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.
...
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3
votes
1
answer
128
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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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2
votes
2
answers
107
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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
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1
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164
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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
2
answers
92
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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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votes
1
answer
139
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Implementing recurrence relation for an integral
I would like to implement the following recurrence relation,
$$I_{n+1}=-\log(2)I_n-\sum_{k=1}^n(-1)^k\left(1-\frac{1}{2^k}\right)\frac{n!\zeta(k+1)}{(n-k)!}I_{n-k}$$
with initial conditions,
$$I_0=\...
- 153
3
votes
1
answer
241
views
How to write a recursive formula?
What is the Mathematica command for the recursive formula:
F[a_]:=Sum[(-1)^a Binomial[a,k] Log[2]^(a-k) F[k], {k,0,a}]
where
...
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4
votes
1
answer
99
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RSolve for system of equations and matrix power [closed]
I have a matrix
a = {{3, -2}, {2, -2}};
We can easily find the n-th power, $A^n$ using
MatrixPower[a,n]
We can also find the ...
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4
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1
answer
170
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How can I compute the $n$-th complete Bell polynomial?
I'm interested in computing the n-th complete Bell polynomial
$
B_n(x_1,..., x_n)
$ using the formula given as the last equation in the "Exponential Bell polynomials" section here (I tried ...
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votes
2
answers
40
views
How to obtain terms defined by a recursion relation in terms of the first value without solving the recursion?
I have a set of coefficients $A_{i}^N$ where $i=0,\dots, N$ that obey a recursion relation that takes the form
$$A_i^N = C_i^N-\sum_{M=1}^N\sum_{k=0}^{N-M}A_k^{N-M}\psi_{i,k}^{N,M}$$
The coefficients $...
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3
votes
1
answer
165
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How is this type of piecewise function represented and calculated? [closed]
How is this type of piecewise function as follows in the picture represented and calculated?
Use:
...
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1
vote
2
answers
120
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Simulating the card game War with $m$ suits and $n$ values
I am trying to simulate the card game War to find approximations to the stopping time distribution for different types of decks, and study conditional probabilities of winning given a certain deck. (...
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1
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2
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80
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Iterate symbolic expression
I'd like to symbolically iterate this formula $1,2,...,n$ times: $$f(z,u)=\frac{z}{1-z}f(z,1)+\frac{zu}{1-zu}f(z,zu)+\frac{z^2u}{1-z^2u}f(z,z^2u).$$
I tried using ...
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0
answers
69
views
Unexpected `LinearRecurrence` behavior in 13.2
From the definitions, I expect LinearRecurrence[{1}, {k}, 10] to be a constant array.
...
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7
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1
answer
278
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Recurrences related to Ramanujan's 1/pi formulas for level 10?
In the course of my research years ago, I came across three integer sequences related to Ramanujan's pi formulas but for level $10$. Their recurrence relations may be important. (Just like the level $...
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2
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99
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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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votes
2
answers
159
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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
1
answer
91
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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3
votes
1
answer
79
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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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2
answers
65
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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
...
0
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1
answer
135
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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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vote
2
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107
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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 ...
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0
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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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1
answer
85
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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 :
...
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7
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4
answers
452
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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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3
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1
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235
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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
2
answers
145
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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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102
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Recursive Sum not evaluating correctly
I'm trying to evaluate the following sums that nest into eachother:
$$
m_k=\frac{k}{k-1} \left(e^{\gamma}+ \sum_{i=1}^{k-2} {k-1\choose i} \frac{m_i}{i} \right)
\\
m_1=e^\gamma
$$
and
$$
\kappa_n = ...
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vote
2
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162
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Recursion with Sum
Using RSolve I tried without success to convert the recursive relation to a non-recursive function. How can I do this?
...
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1
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104
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Plot of a recursive expression having a parameter
I have a recursive expression defined as
$$
h_u= (1-a)(1-b) h_{u-1} + \sum_{k=2}^{u-1} (1-a) b h_{u-1-k} - \sum_{k=2}^{u} h_{u-k} - \sum_{k=1}^{u+1} \Lambda_{u,k}
$$
where $\Lambda_{u,k} = \sum_{m=u-k+...
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votes
1
answer
110
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Evaluate a double sum using Mathematica
I am evaluating using Mathematica, the double sum $\sum_{u=0}^\infty \lbrace \sum_{k= u+1}^{u+y}[\dfrac{(1-a)}{4} (3/4)^k + 3a[(\dfrac{1}{2})^{k-1} - (\dfrac{3}{4})^{k-1} ]\rbrace $, where $'a' $ is a ...
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