All Questions
20
questions
3
votes
2
answers
61
views
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 ...
- 131
4
votes
1
answer
170
views
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 ...
- 45
1
vote
2
answers
80
views
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 ...
- 203
1
vote
1
answer
104
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+...
- 53
2
votes
1
answer
116
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?
...
- 23
1
vote
1
answer
117
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 ...
- 251
0
votes
1
answer
90
views
Finding the exact symbolic formula for a function defined recursively
Let me introduce the problem.
I have the following functions;
The first one is defined recursively
$h(i,j):=\frac{i-1}{j+1}h(i+2,j-2)$ and $h(i,0)=1$ where $i$ and $j$ are even integers, greater than $...
- 391
0
votes
0
answers
113
views
How to convert a symbolic recursive formula to a non-recursive one
I am new to Mathematica. I want to convert a recursive formula to a non-recursive one using symbolic math. Specifically, I have a recursive formula similar to this:
$a_n = f_a(c_{n-1}, x_{n-1})$
$...
- 101
4
votes
2
answers
492
views
RSolve not reducing for a certain recurrence relation
I'm trying to use RSolve as follows to solve a recurrence relation:
...
- 143
1
vote
1
answer
97
views
Recurrences with some relation to Dedekind eta functions
Dedekind eta functions are know to satisfy certain difference equations/recurrence relations. The same is true for ratios of eta functions. Suppose some ratio of eta functions, say $A(q)$ satisfies ...
- 365
3
votes
1
answer
279
views
RSolve does not work as expected
Why am I getting error
The arguments should be ordered consistently
for the following code:
...
- 31
2
votes
1
answer
122
views
Is it possible to get a symbolic a concise expression for my function?
Suppose I have ordered rank-4 indices $1\le i<j<k<l\le n$, where $n$ is a fixed but unspecified integer. I define a function $s(n)$ as follows:
$$s(n)=\sum_{1\le i<j<k<l\le n}(-1)^{\...
- 197
4
votes
2
answers
279
views
Symbolic comparison of recursive functions
I would like to test two recursive functions for equality for all arguments. So far I have this:
f[0]:=1
f[n_] := n f[n - 1]
ForAll[x, x>=0, f[x]==f[x]]
...
3
votes
1
answer
219
views
Solve a set of recurrence relations with a constraint
I am trying to solve a set of recurrence equations as given below:
$p_{1, n}*(l + n*u1) = p_{1, n-1}*l + p_{1, n+1}*(n+1)*u1 + p_{2, n}*u2$,
$p_{2, n}*(l + n*u1 + u2) = p_{2, n-1}*l + p_{2, n+1}*(n+...
- 55
4
votes
2
answers
177
views
How can I find the coefficients of the next recursive symbolic function?
I have the following function
$$
f(x+3k) = -mf(x+2k)+f(x)
$$.
If we get $x=x+k$, then
$$
f(x+4k) = -mf(x+3k)+f(x+k) = m^2f(x+2k)+f(x+k)-mf(x)
$$. Also we obtain the coefficients of the final functions,...
- 442