Questions tagged [recursion]
For questions about defining recursive functions, recursive algorithms and solving recursive equations.
659
questions
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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 ...
- 283
0
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0
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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
$$
\kappa_n = ...
- 11
1
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2
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162
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Recursion with Sum
Using RSolve I tried without success to convert the recursive relation to a non-recursive function. How can I do this?
...
- 593
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1
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104
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Plot of a recursive expression having a parameter
I have a recursive expression defined as
$$
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}
$$
where $\Lambda_{u,k} = \sum_{m=u-k+...
- 53
2
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1
answer
110
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Evaluate a double sum using Mathematica
I am evaluating using Mathematica, the double sum $\sum_{u=0}^\infty \lbrace \sum_{k= u+1}^{u+y}[\dfrac{(1-a)}{4} (3/4)^k + 3a[(\dfrac{1}{2})^{k-1} - (\dfrac{3}{4})^{k-1} ]\rbrace $, where $'a' $ is a ...
- 53
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4
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322
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Factorial implementation using FixedPoint
I implemented the factorial function:
fact[0] = 1
fact[x_Integer?Positive ] := x*fact[x - 1];
f[4] yields 24 as expected
I tried a different version of the ...
- 1,698
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64
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Compile error in recursive code due to large integer
I am trying to implement a compiled version for the original algorithm that is supposed to run faster . It works fine for small iteration loop number when max=100. However, when loop number gets ...
- 893
2
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1
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116
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Implement recursion one step at a time with a function of more than one variable
i am trying to implement a recursive difference equation step by step, by implementing rules, similar to Rojo's method in this thread: How can I evaluate only a single step of a recursive function?
...
- 23
3
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2
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389
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Recursive function in Mathematica
I need to implement the following recursive function in Mathematica.
$$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 $a=0$, ...
- 1,225
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292
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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:
...
- 149
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2
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325
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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,
...
- 17.2k
1
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0
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93
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) | ...
- 251
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82
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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 $k$ ...
- 101
1
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1
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117
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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 ...
- 251
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1
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132
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Pattern match with "+" sign
Can you pattern match with a "+" sign?
Here is the recursion...(which does not work)
...
- 437