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Questions tagged [summation]

Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence

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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 ...
Hawi's user avatar
  • 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: ...
FDP's user avatar
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0 answers
60 views

Clebsch–Gordan coefficient calculation for L-S basis in system of three particles

I am trying to calculate eq (A3) ...
Anshul Bokade's user avatar
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 ...
Maesumi's user avatar
  • 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 ...
Ahmed Riza's user avatar
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: ...
Felipe's user avatar
  • 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}...
Marco's user avatar
  • 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^...
psl2Z's user avatar
  • 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 ...
Felipe's user avatar
  • 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 (...
user29859's user avatar
  • 145
1 vote
1 answer
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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}\...
user29859's user avatar
  • 145
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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 ...
A P's user avatar
  • 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}] ...
user64494's user avatar
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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 ...
Felipe's user avatar
  • 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 ...
Jie Zhu's user avatar
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'KroneckerDelta' won't evaluate symbolically

I'm trying to get Mathematica to symbolically evaluate sums containing KroneckerDelta. It picks out the correct term when comparing the index agains a number, but ...
Fii's user avatar
  • 101
3 votes
0 answers
60 views

Weird summation result computing the expectation of Poisson random variable

Can you explain the obtained difference between these two rapidly convergent infinite sums? The correct answer is $-1/2$, and this should be obtained in both presented cases. ...
Fancier of Mathematica's user avatar
0 votes
0 answers
33 views

Making NSum faster with higher precision and accuracy

I have the following code that I want to run to obtain a cumulative list out of various values of s1=3 to s1=10 (say) for the ...
QFTheorist's user avatar
4 votes
2 answers
319 views

Get cumulative sums in a list without using a for loop [closed]

I want a list of the kind list = {a,a+b,a+b+c} for list plotting. The quantities of the list come from a function. Let us say this is ...
QFTheorist's user avatar
0 votes
1 answer
56 views

Convergent Taylor series unrecognized by Sum

I am trying to understand why Sum does not recognize a particular Taylor series as convergent. I have defined a function 'series' like this, that computes the Taylor series of a function 'f' at 'x', ...
Glenn Welch's user avatar
0 votes
1 answer
55 views

NSum with variable sitting inside

I want to evaluate the following and many other similar expressions numerically from k=2 to k=Infinity with a variable ...
QFTheorist's user avatar
5 votes
1 answer
286 views

Mathematica failing to evaluate sum

I have some sums to simplify/evaluate, but for some reason I can't even get Mathematica to simplify relatively simple sums. For example, I tried to get Mathematica to simplify this sum: $$\sum_{k=0}^{...
Oliver's user avatar
  • 51
2 votes
0 answers
41 views

Take symbolic derivative of summation expression and display as unexpanded sum

My main problem here is two-fold: Take symbolic derivative of summation expression Stop summations from being "unrolled"/expanded, e.g., displayed as the sum of terms I also have some ...
ImagineBaggins's user avatar
5 votes
1 answer
283 views

Mathematica stuck for more than 12 hours on getting numerical value

The following expression when summed from $k=0$ to $\infty$ converges but returns an absolutely hideous expression that I cannot fit in here due to the character limit. I want the numerical value up ...
QFTheorist's user avatar
0 votes
0 answers
24 views

Optimal way of defining sums-linear function [duplicate]

I asked on a previous post how to define a function which satisfies $f[x+y]=f[x]+f[y]$ and then define $f[x]$ on monomials. The problem with this is that it involves a lot of iterations when we ...
Adrien Martina's user avatar
0 votes
0 answers
66 views

Generic sums in Mathematica [duplicate]

I would like to treat sums in very generic manners, but it looks like mathematica is very bad at that. For example, it cannot simplify to zero such expressions : ...
Adrien Martina's user avatar
8 votes
2 answers
189 views

Incorrect answer given by Sum

Is this a bug? Sum[Binomial[2 n - 1, 2 m - 1]*(L - 2 - 2*(2 m - 1)), {m, 1, n}] gives -4^(-1 + n) (1 - L + 2 n) However, ...
Jake Pan's user avatar
  • 526
5 votes
1 answer
258 views

Quantum Field Regularization: Choice between ExpIntegralE and Gamma for Casimir Effect

For the Casimir effect with exponential regularization, we compute the vacuum energy between the plates (somewhat simplified) with: $$\omega = c\ \sqrt{q^2+k_z^2}$$ $$ E = \sum_{k_z=n\pi/a} 2 \int\...
Jos Bergervoet's user avatar
0 votes
1 answer
56 views

How to add a condition to a double summation

I want to write the following equation in Mathematica, but I don't know how to do that
ahmed's user avatar
  • 85
1 vote
0 answers
50 views

Simple `Sum` evaluating wrong [closed]

I want to make a table of values for the sum Sum[\[Phi][x - i*j], {j, 1, x}, {i, 1, x}] I want to include non-integer values of ...
Richard Burke-Ward's user avatar
0 votes
0 answers
65 views

Plot of a complicated function under double summation

I wrote the following inputs in mathematica to plot the following expression: ...
R. Bhattacharya's user avatar
4 votes
1 answer
100 views

Making Mathematica return the full simplified expression by default

I have an expression defined as ...
QFTheorist's user avatar
0 votes
0 answers
52 views

How to monitor "Sum" in order to estimate the time of "Sum"?

I am dealing with a Sum on a large scale, which can not run out an answer on my computer. I want to know if there is some command that allow me to monitor the ...
Lomath's user avatar
  • 119
2 votes
3 answers
135 views

Issue in the calculus of inverse of terms from a list

to begin i want to warn you that i am a beginner in mathematica. I have to create a function that calculates the impedance total of an association of n (electronical) components. So the formula is 1/Z(...
ShoupinouZz's user avatar
3 votes
1 answer
151 views

Summation question?

I have following summation that I want to implement using Mathematica: ...
Vayne's user avatar
  • 101
1 vote
1 answer
36 views

How to add two data tables of unequal length to plot a curve which should be sum of table1 plus table 2?

I am facing a problem but Suppose just for an example below, i am mentioning the dummy code of the problem; ...
Immy Salam's user avatar
1 vote
2 answers
139 views

Should expression evaluation depend on the choice of a variable name?

I am verifying the series representation of the Sonine polynomial or the associated Laguerre polynomial, which is $$ L_m^{(n)}(x)=\sum\limits_{l=0}^n\left(-1\right)^l\binom{m+n}{m-l}\frac{x^l}{l!}=S_{...
houzw's user avatar
  • 811
11 votes
5 answers
2k views

Why does Mathematica not recognize a convergent series?

Bug introduced in 12.1, persisting through 13.2 or later In one of my program run on Wolfram Cloud I run the command: Sum[(-1)^(Floor[k/2])/(k+1),{k,0,Infinity}] ...
drer's user avatar
  • 719
0 votes
1 answer
79 views

Triple Summation Calculation Which Includes an Integral

I am a beginner in Mathematica. I have to calculate the following summation:$$C_3(\alpha)=\frac{1}{3}\sum_{j,k,l=3}^{\infty}(2j+1)(2k+1)(2l+1)(C_jC_k+C_kC_l+C_lC_j)f_{jkl}$$ where $$f_{jkl}=\frac{1}{4\...
Rosstopher's user avatar
1 vote
1 answer
84 views

Value of a function over permutations of two lists

I want to do the sum (in Ising lattice gauge theory) ...
QFTheorist's user avatar
1 vote
1 answer
54 views

Sum on a lattice where variables can only take two values (Ising lattice gauge theory)

I want to study the Ising Gauge Theory which has the Hamiltonian \begin{equation} \mathcal{H} = -J \sum_{n,\mu,\nu} \sigma_3(n,\mu)\sigma_3(n+\mu,\nu)\sigma_3(n+\mu+\nu, -\mu)\sigma_3(n+\nu, -\nu) \...
QFTheorist's user avatar
6 votes
4 answers
479 views

Discrepancy Between Mathematica Result and True Result in Special Cases

Let's define sum1N[m_] := Sum[Cos[x - 2 n Pi/NN]^m, {n, 1, NN}] // Simplify When m=4, we get (3 NN)/8 However, if we compute ...
Ping Chia's user avatar
1 vote
0 answers
66 views

Why this Solve cannot be solved [duplicate]

Solve[Sum[p*a[i], {i, 1, n}] == 0, p, Reals] Solve[p*Sum[a[i], {i, 1, n}] == 0, p, Reals] The first line of code cannot be solved, but when the variable ...
Yilin Cheng's user avatar
0 votes
1 answer
55 views

How can i create an equation with a sum? [closed]

I have a list of $p_i$ and the condition that $\sum_{i=0}^{i=69} p_i = 1 $ I also have a list of 69 other different equations. I want to use NSolve to solve for the ...
100xln2's user avatar
  • 437
0 votes
1 answer
86 views

How to write function series in Mathematica?

How do I write the function given below as a mathematical function: $\Sigma^{8}_{i=1}\Sigma^{8}_{j=1}c_{ij}\lambda_i \otimes\lambda_j$ I have the values of $\lambda_i$ and $\lambda_j$.They are 3x3 ...
Lelouch's user avatar
  • 121
0 votes
0 answers
77 views

How to use the previous value in Sum?

I am trying to do a summation with repeated calculations in the "probability" variable, which cost a lot of time. However, in each sum, the "probability" can be calculated from the ...
Lomath's user avatar
  • 119
0 votes
0 answers
47 views

FindMinimum with many Sums and NIntegrates is very slow

I want to calculate the global minimum of an equation which has several hundred Sums (I used 300 in this code), but the calculation is very slow. My code is as ...
user43830's user avatar
  • 101
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 ...
Dotman's user avatar
  • 496
1 vote
1 answer
130 views

Using "Table[]" to create a matrix without submatrices [duplicate]

I'm trying to create a certain 6x6 matrix using Mathematica's in-built "Table[]" function and have landed on ...
ConfusedCabbage's user avatar
2 votes
0 answers
149 views

Finite sum of complex exponentials giving wrong result [closed]

I was playing with the following sum: $$ \sum_{k=0}^{2} e^{\frac{2\pi i k^2}{3}} = e^{0} + e^{\frac{2\pi i}{3}} + e^{\frac{8\pi i}{3}} \ne 0, $$ which is non-zero, at least according to Wolfram|Alpha. ...
Sidharth Ghoshal's user avatar

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