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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6 votes
2 answers
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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
  • 506
3 votes
1 answer
191 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
50 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
  • 75
1 vote
0 answers
49 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
5 votes
1 answer
95 views

Making Mathematica return the full simplified expression by default

I have an expression defined as ...
QFTheorist's user avatar
0 votes
0 answers
51 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
134 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
126 views

Summation question?

I have following summation that I want to implement using Mathematica: ...
Vayne's user avatar
  • 81
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
133 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
  • 338
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
78 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
80 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
51 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
478 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
63 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
51 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
  • 427
0 votes
1 answer
83 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
  • 21
0 votes
0 answers
68 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
45 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
106 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
  • 424
1 vote
1 answer
128 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
143 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
1 vote
2 answers
184 views

Incorrect sum behavior over a range

What is going on here? ...
rogerl's user avatar
  • 4,209
3 votes
1 answer
151 views

Creating a plot for a summation function

I have this potential function which I believe is representative of a grounded cube in a 3D plane. I'm not entirely sure if this is it, but here is the general solution of the function: v(x,y,z) = G(...
Carson Joseph's user avatar
1 vote
0 answers
48 views

Plot of some complicated functions containing special functions under both Sum and Product

I am trying to plot the $|f(\theta,\phi)|^2$, where the expression of $f(\theta,\phi)$ is as under: $$ f =\sum_{n_j}\Pi_{j_x,j_y,j_z}P_{n_j}\sum_{l}A_s \text{e}^{-ia(l_1q_x+l_2q_y+l_3q_z)}\times \...
R. Bhattacharya's user avatar
1 vote
3 answers
194 views

Function for an n-fold sum

I have sums of the form $\sum_{j=1}^{3}\sum_{k=j+2}^{5} b_j b_k,\quad \sum_{j=1}^{3}\sum_{k=j+2}^{5}\sum_{m=k+2}^{7} b_j b_k b_m, \quad \dots$ and so forth. I am now trying to find a function that ...
qising's user avatar
  • 43
3 votes
1 answer
224 views

Thermodynamics of the 2D Ising model

I want to study the thermodynamics of the 2D Nearest Neighbour Ising model (calculate the average energy, susceptibility, etc.). I have the Hamiltonian $$\mathcal{H} = J\sum_{\langle i j \rangle} s_i ...
QFTheorist's user avatar
3 votes
1 answer
372 views

Sum works with 1000000, fails with 2000000 - bug?

Consider the following: ...
rogerl's user avatar
  • 4,209
0 votes
1 answer
94 views

Numerical Integration of a Complicated Function

I am evaluating the numerical integration it takes very much long time. Can somebody suggest to improve the code? Code runs smoothly for the first plot given by h1. ...
Assad Hafiz's user avatar
1 vote
0 answers
113 views

Simple sum gives complicated answer

If $a$ is real and $b$ is complex, then this sum is easy to do by hand: Sum[E^(I n a)/(n + b), {n, -∞, ∞}] ...
Quasar Supernova's user avatar
1 vote
2 answers
96 views

Complex infinity when using Fullsimplify to sum

I am trying to simply and speed up a sum using Fullsimplify, when I try the simplified expression with a simple example, it comes up with Complex infinity. How do the Fullsimplify itself give an ...
Lomath's user avatar
  • 119
3 votes
1 answer
231 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 ...
Ali Shadhar's user avatar
4 votes
1 answer
105 views

Building projection operators efficiently

The projection operator $P$ is defined in quantum mechanics as $$ P=\sum_i^n \vert\psi_i\rangle \langle \psi_i\vert, $$ where $\vert\psi_i\rangle$ is a column vector and $(\langle \psi_i\vert=(\...
wooohooo's user avatar
  • 289
0 votes
1 answer
68 views

Mathematica giving different results from Sum when I expand the sum and evaluate some terms separately

Here we have the initial sum T1[m,n], then I removed the one term (k) and completed the exact sum and the remainder sum called T2[m,n]. T1[m,n] and T2[m,n] should be identical. The test in the table ...
Lorenz H Menke's user avatar
1 vote
1 answer
221 views

Discrepancy with Hurwitz Zeta function

I've come across an issue while using Wolfram Mathematica that I don't quite understand. Consider the following symbolic computation: ...
stefan_chem's user avatar
0 votes
2 answers
129 views

How to prevent the computation of this polynomial sum?

In my research project, I'm working with the following polynomial $$p(x) = 1 + 2x + 3x^2 + \ldots + nx^{n-1} + nx^n + nx^{n+1} + (n-1)x^{n+2} + (n-2)x^{n+3} + \ldots + 2x^{2n-1} + x^{2n}$$ or $$nx^n +\...
wol's user avatar
  • 3
4 votes
2 answers
202 views

Simple sum runs endlessly

I tried evaluating Sum[-(1/(2 X (-X+vF (I+y) (I T+n β))^3)),{n,-∞,∞},GenerateConditions->False] which did not terminate. Whereas the modified sum ...
Quasar Supernova's user avatar
0 votes
1 answer
64 views

These expressions give different results, how can I filter out the error?

Sum[E^(a x + b x) /. a -> 1 /. b -> -1, x] Sum[E^(a x + b x), x] /. a -> 1 /. b -> -1 First one returns x, second ...
Anixx's user avatar
  • 3,575
4 votes
1 answer
104 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 ...
Robert Lee's user avatar
2 votes
2 answers
100 views

Assumptions in Sum

I am calculating the following ...
mattiav27's user avatar
  • 6,637
2 votes
3 answers
136 views

Accumulate Date Data Over Some Period

Say I have a series of time points, spread randomly throughout the year ...
Tomi's user avatar
  • 4,366
8 votes
2 answers
211 views

Why is `k` in the output of `Sum[Log[k]^2/k^k, {k,1,Infinity}]`?

The following sum converges to a constant. It would be much better to return unevaluated than to return something incorrect. ...
Vaclav Kotesovec's user avatar
2 votes
2 answers
267 views

How to write the following summation in Mathematica?

How to write the following summation in Mathematica? where is n integer. My try: (But it does not work) ...
RF_1's user avatar
  • 672
1 vote
1 answer
56 views

Redundant cases from Sum

I am new to Mathematica. I would like to understand why Mathematica returns redundant cases, and whether it is possible to simplify them to the generic case $(n>1)$ that covers everything $(n\ge0)$....
Andras Vanyolos's user avatar
3 votes
2 answers
89 views

What is the meaning of adding/subtracting a fraction in a summation limit inside a limit?

In Wolfram Alpha entry 1 the following is claimed to be true: $$\lim_{n\to \infty } \left(\sum _{k=1}^n \log (2 k)-\sum _{k=1}^{n+\frac{1}{2}} \log (2 k-1)\right)=\frac{1}{2} \log \left(\frac{\pi }{2}\...
Mats Granvik's user avatar
  • 1,159
0 votes
1 answer
28 views

sum elements (variables) of a vector variable [closed]

I would like to sum elements of a vector variable, e.g., Is xvec = Array[x, 10] s24 = Sum[xvec[i], {i, 2, 4}] where $s_{24}:=\sum_{i=2}^4 x_i$. However, I am ...
rrrrr's user avatar
  • 125
0 votes
0 answers
59 views

How to optimize this multiple sums?

I need to perform this sum $$ \sum_{n_1=1}^{\infty} \sum_{n_2=1}^{\infty} \sum_{n_3=1}^{\infty} \sum_{n_4=1}^{\infty} \frac{K_{1} \left(\frac{a}{x} \sqrt{n_1^2 + 4 y_2^2 x^2 n_2^2 + 4 y_3^2 x^2 n_3^2 +...
Lucas Gondim's user avatar
0 votes
1 answer
43 views

The `Exponent` of some expressions with `Sum`

Why the following code does not give T where T is a positive integer? Exponent[Sum[Subscript[A, i]*f[x]^i, {i, 0, T}], f[x]] or ...
HD239's user avatar
  • 543

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