All Questions
23
questions
0
votes
3
answers
112
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 ...
- 496
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
...
- 505
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
0
votes
0
answers
102
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
$$
\kappa_n = ...
- 11
1
vote
2
answers
162
views
Recursion with Sum
Using RSolve I tried without success to convert the recursive relation to a non-recursive function. How can I do this?
...
- 593
2
votes
1
answer
110
views
Evaluate a double sum using Mathematica
I am evaluating using Mathematica, the double sum $\sum_{u=0}^\infty \lbrace \sum_{k= u+1}^{u+y}[\dfrac{(1-a)}{4} (3/4)^k + 3a[(\dfrac{1}{2})^{k-1} - (\dfrac{3}{4})^{k-1} ]\rbrace $, where $'a' $ is a ...
- 53
2
votes
4
answers
278
views
what's the Mathematica command for a recursive formula?
I want to know the Mathematica command for
$$f(a)=\sum_{n=0}^{a-1} \frac{f(n)}{n!}, \quad f(0)=1$$
How to write $f(0)=1$ together with the summation? I used:
...
- 505
0
votes
0
answers
154
views
How can I speed up this pdf path integration calculation with a slow recursive function with 40^4 summed terms in each iteration?
I am writing a path integration code for a numerical approximation to a probability density function.
I essentially take some initial continuous probability density function p0 and then perform a ...
- 21
0
votes
1
answer
90
views
Finding the exact symbolic formula for a function defined recursively
Let me introduce the problem.
I have the following functions;
The first one is defined recursively
$h(i,j):=\frac{i-1}{j+1}h(i+2,j-2)$ and $h(i,0)=1$ where $i$ and $j$ are even integers, greater than $...
- 391
9
votes
0
answers
214
views
Sum causes a recursion problem
Bug introduced in 8 or earlier and Fixed 13.3.1
Sum[((-1)^(i + 1)*Binomial[n, i]*(n - i)!)/n!, {i, 1, n}]
This cause a Recursion problem.
As the comment said, If ...
- 10.1k
4
votes
2
answers
426
views
Faster, More Elegant Way to Produce a Recursive Sequence of Rational Numbers [closed]
I am studying a recursion below:
$$B_{N,0}=1$$
$$B_{N,k}=-\binom{N+k}{k}^{-1}\sum_{j=0}^{k-1}\binom{N+k}{j}B_{N,j}$$
Now I'm not great at writing in Mathematica. It's been a while since I've used it. ...
- 501
1
vote
0
answers
115
views
Getting NSum to go to the right depth in recursive definitions
I wanted to produce some plots of the action of the Gauss shift map on cumulative distribution functions. This means I wanted to plot functions $F_n(x)$, for $0 \leq x \leq 1$, defined by $F_1(x) = x$ ...
- 1,552
2
votes
2
answers
449
views
Implement a recursive formula with internal sum
I need to calculate following recursion formula.
I implemented this in MATHEMATICA as follows:
But it always gives errors for $k>0$. Can someone help me to implement this?
...
- 325
2
votes
3
answers
559
views
Sum with variable terms to sum over
Suppose I have a polynomial like this:
$$a=x_{j_1} + x_{j_1}x_{j_2} + x_{j_1}x_{j_2}x_{j_3} + ...+x_{j_1}x_{j_2}x_{j_3}...x_{j_n}$$
I want to create a function that takes this polynomial and does the ...
0
votes
0
answers
48
views
Speeding up multiple conditional summations
I have situation where I have a matrix H, and want to build a set of ODEs dependent on the values of the eigenvalues, let me illustrate:
...
- 81