Questions tagged [recursion]

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

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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. ...
SurvivalWish's user avatar
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1 answer
75 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. ...
Math_student's user avatar
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2 answers
175 views

Sorting a list of functions by exploiting the recursive structure

Given a list of functions list and a vector of arguments {t, a}: ...
Tugrul Temel's user avatar
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2 answers
134 views

Symbolic recursion

I have the two recursive relations: ...
Math_student's user avatar
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3 answers
105 views

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 ...
Dotman's user avatar
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0 answers
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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. ...
LambdaHaskell's user avatar
3 votes
1 answer
127 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 ...
CasperYC's user avatar
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2 votes
2 answers
104 views

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 ...
Hugo Andrade's user avatar
1 vote
1 answer
156 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 ...
Russell Jay Hendel's user avatar
1 vote
2 answers
70 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: ...
Neill Clift's user avatar
5 votes
1 answer
120 views

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=\...
bob's user avatar
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1 answer
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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 ...
Ali Shadhar's user avatar
4 votes
1 answer
91 views

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 ...
Moo's user avatar
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4 votes
1 answer
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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 ...
Robert Lee's user avatar
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Solution to a vector recurrence equation

Suppose $n\ge1$ is fixed. Let $C_1,C_2,\ldots,C_n$ be given constants. Consider the recurrence $$ C_n[S_{1}^{(n)},S_{2}^{(n)},\ldots,S_{n-1}^{(n)}]= \left[\binom{n}{1},\binom{n}{2},\ldots,\binom{n}{n-...
Alex's user avatar
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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 $...
user1620696's user avatar
3 votes
1 answer
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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: ...
csn899's user avatar
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1 vote
2 answers
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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. (...
Teg Louis's user avatar
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1 vote
2 answers
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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 ...
Daniel Checa's user avatar
2 votes
0 answers
63 views

Unexpected `LinearRecurrence` behavior in 13.2

From the definitions, I expect LinearRecurrence[{1}, {k}, 10] to be a constant array. ...
vapor's user avatar
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7 votes
1 answer
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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 $...
Tito Piezas III's user avatar
1 vote
2 answers
86 views

SummaryBox and Recursion

How can I make it so that what is under the dropdown block is not calculated/constructed at once? Example code: ...
Kirill Belov's user avatar
3 votes
2 answers
153 views

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, ...
Vicente Sepúlveda Trivelli's user avatar
1 vote
1 answer
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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. ...
Thomas 's user avatar
3 votes
1 answer
74 views

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 ...
HE TANG's user avatar
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2 answers
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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 ...
Андрей Кокорев's user avatar
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1 answer
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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 ...
s_mondal's user avatar
1 vote
2 answers
98 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 ...
Jason Ham's user avatar
9 votes
0 answers
605 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 ...
Nasser's user avatar
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1 answer
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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 : ...
Anna MSJ's user avatar
7 votes
4 answers
439 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 ...
martin's user avatar
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3 votes
1 answer
221 views

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 ...
TheInvisibleParticle's user avatar
1 vote
2 answers
137 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 ...
Matteo's user avatar
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0 answers
101 views

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 = ...
Mick Stukes's user avatar
1 vote
2 answers
132 views

Recursion with Sum

Using RSolve I tried without success to convert the recursive relation to a non-recursive function. How can I do this? ...
granular bastard's user avatar
1 vote
1 answer
103 views

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+...
Rosy's user avatar
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2 votes
1 answer
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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 ...
Rosy's user avatar
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3 votes
4 answers
317 views

Factorial implementation using FixedPoint

I implemented the factorial function: fact[0] = 1 fact[x_Integer?Positive ] := x*fact[x - 1]; f[4] yields 24 as expected I tried a different version of the ...
Michel's user avatar
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0 votes
0 answers
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Compile error in recursive code due to large integer

I am trying to implement a compiled version for the original algorithm that is supposed to run faster . It works fine for small iteration loop number when max=100. However, when loop number gets ...
Aschoolar's user avatar
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2 votes
1 answer
103 views

Implement recursion one step at a time with a function of more than one variable

i am trying to implement a recursive difference equation step by step, by implementing rules, similar to Rojo's method in this thread: How can I evaluate only a single step of a recursive function? ...
StevieP's user avatar
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3 votes
2 answers
278 views

Recursive function in Mathematica

I need to implement the following recursive function in Mathematica. $$F[-2*a,b,2b;2]=\left(\frac{a-1/2}{a-1/2+b}\right)F\left[-2*(a-1),b,2b;2\right]$$ The conditions of the functions are: if $a=0$, ...
Jasmine's user avatar
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4 votes
3 answers
276 views

How to create a sequence of functions defined recursively?

I'm trying to create a Table of functions where each new element is defined recursively via indefinite integration of the previous one. I've tried doing: ...
TC159's user avatar
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2 votes
2 answers
321 views

Why does System`Private`ConstructNoEntry[Quantity, 1, "kg"] enter a Recursion?

System`Private`ConstructNoEntry[BesselJ, 0, x] works fine, and outputs BesselJ[0, x] However, ...
matheorem's user avatar
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1 vote
0 answers
81 views

Solving a 2D recurrence diagonal-by-diagonal

I have a 3D recurrence relation -- which I know can be hard for Mathematica to work with, so I boiled it down to 2D. We have two functions, $f_1(i,j)$, $f_2(i,j)$ defined on the state space $\{(i,j) | ...
black's user avatar
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0 votes
0 answers
77 views

How to do this recursion relation in Mathematica effectively?

I have a function $h_{\Delta,l}(r,\eta)$ satisfying \begin{equation} h_{\Delta,l}(r,\eta)=\tilde{h}_{l}(r,\eta)+\sum_{k}\frac{c(k)}{\Delta-(1-l-k)}r^{k}h_{1-l+k,l+k}(r,\eta) \end{equation} where $k$ ...
Vayne's user avatar
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1 vote
1 answer
110 views

RSolve with integer and boolean variable

I have a recurrence relation with two variables $i, b$ where $i \in \{0, \ldots, n-1\}$ for some parameter $n \in \mathbb{N}$; and $b\in \{0,1\}$. I tried to solve it using RSolve, but the function ...
black's user avatar
  • 251
2 votes
1 answer
129 views

Pattern match with "+" sign

Can you pattern match with a "+" sign? Here is the recursion...(which does not work) ...
PiE's user avatar
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1 vote
0 answers
100 views

Why Mathematica don't set \$RecursionLimit and \$IterationLimit very big by default? [closed]

For my current program in Mathematica, sometimes I will encounter an error regarding \$IterationLimit and \$RecursionLimit. So I always set these two numbers to very large at the starting of every ...
Canonical's user avatar
0 votes
1 answer
38 views

Recursive error encountered when updating rules of assignment [closed]

I'm working on a problem which requires associating a single (complex) number with a pair of binary vectors. I'm doing this by creating a set of assignments through a function I call ...
miggle's user avatar
  • 647
2 votes
3 answers
161 views

Solving equation with delay term

I am trying to solve an equation looks like this... x[t] == t^2 + x[t-10] How can I obtain a numerical solution for x[t] in Mathematica? Thanks.
Matt Chen's user avatar

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