Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
1,003
questions
0
votes
1
answer
62
views
Finding a sequence function
I would appreciate your help in finding a polynomial sequence function based on a set of data points. For each pair of integers {j, k}, I have the following data points
...
- 173
0
votes
0
answers
76
views
Troublesome output of summation's derivative
I am trying to compute a derivative of a nested sum, but I can't avoid Mathematica to output Kronecker deltas and unexpected cases on complex numbers.
Consider the following setting:
...
- 3
0
votes
0
answers
60
views
Clebsch–Gordan coefficient calculation for L-S basis in system of three particles
I am trying to calculate eq (A3)
...
3
votes
1
answer
58
views
Double sum error message for NSum
I am attempting to evaluate
NSum[1/((2 i + 1)^4 + (2 j + 1)^4), {i, -1000, 1000}, {j, -1000, 1000}]
but it gives a negative value as the result; alongside an error ...
- 807
4
votes
3
answers
167
views
Recurrence relation with a sum
Say we have the following recurrence:
$$T[n] = \sum_{j=1}^{n-1} 2 T[j] T[j-1], \forall n > 1$$
with $$T[0] = T[1] = 2$$
I tried RecurrenceTable but that does not ...
- 43
2
votes
1
answer
69
views
How to use Sum properly to avoid problems when the summating limits are undefined?
I'm struggling in the use of Sum.
I want to define something like that:
...
- 165
1
vote
1
answer
103
views
Derivative of a summation
I need to take the derivative of $\sum_{x=1}^{M}\sum_{a=0}^{J-1}\sum_{t=0}^{\infty}u(c(x,t+a,a),l(x,t+a,a))$ for a generic $c(y,s,b)$, or in other words:
$$\frac{\partial}{\partial c(y,s,b)} \sum_{x=1}...
- 13
2
votes
1
answer
128
views
Why can't Mathematica compute the series $\sum_{n=1}^{\infty} \frac{\mu(n)}{e^{2n}-1}$?
Why can't Mathematica 14 compute the series $$\sum_{n=1}^{\infty} \frac{\mu(n)}{e^{2n}-1}$$
where $\mu$ is the Möbius function? The series is obviously absolutely convergent (summands dominated by $2e^...
- 123
2
votes
0
answers
103
views
Sum doesn't work as I expected
I'm trying to sum a bunch of polynomials. I'm implementing that:
Sum[Subscript[P, k][c] (k + x) z^(k + x), {k, -x, -1}]
and mathematica gives me back that
I ...
- 165
1
vote
2
answers
73
views
Breaking multiple summations of terms in single term summations
I have a question which is a follow-up of a previous one: Break summation of terms in summations of each term.
I noticed that using Distribute on a summation (...
- 145
1
vote
1
answer
55
views
Break summation of terms in summations of each term
I am trying to break the summation over two terms in two summations for each term, that is:
From \begin{align}\sum\limits_{l}^{L}a_{l}^2(-t_{l}t_{x} + t_{l}^2t_{x})&\end{align} to \begin{align}\...
- 145
0
votes
0
answers
58
views
Efficient Computation of Nested Sums
I have $\sum_{i=1}^na_i(x)\sum_{\nu=0}^Nb_\nu(x)\sum_{k=0}^\nu c_k(x)\sum_{l=0}^kd_l(x) \sum_{j=0}^l e_j(x)$ where $n=2000$ and $N=70$ and the $a_i$, $b_\nu$, $c_k$, $d_l$, $e_j$ are all functions ...
- 225
1
vote
1
answer
102
views
How to derive a closed-form expression for the sum of this series?
Mathematica 14.0 on Windows produces
Sum[x^(9 + 6 k)/(9 + 6 k)!, {k, 0, Infinity}]
...
- 27.3k
0
votes
0
answers
75
views
Is there an easy way to understand how to manipulate summations?
I'm working in a very very long calculation that could be done by hand but it might be tedious. Moreover, when doing by hand that amount of calculations I'm subject to errors, of course. Then I ...
- 165
11
votes
2
answers
690
views
Bugs with `Sum`?
In this post, I provided a solution to the integral $$\int_0^{\infty}\left[\int^1_0J_0(v\rho)\cos(\rho^2/2)\rho\,\mathrm{d}\rho \right]^2v\mathrm{d}v$$
However, I found a bug with ...
- 1,811