Questions tagged [summation]

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

Filter by
Sorted by
Tagged with
1 vote
0 answers
73 views

Suggestions to simplify and perform the summation of a complicated expression

I have a very complicated expression involving Hermite polynomials of complex variables, exponential and hyperbolic functions. Since it is too long to be pasted here, you can find the expression here. ...
user avatar
0 votes
1 answer
55 views

How can one plot a sum in mathematica? [closed]

I would like to plot the following answer to the heat equation, Sum[(((-1)^n - 1)/n^2) Cos[n x] Exp[-(n^2 t)], x] But since it is a sum, it does not appear to work....
user avatar
  • 269
1 vote
0 answers
38 views

Do summation if factor does not depend on index

I have the following sums $$\sum _{j=0}^{n-1} \left(\sum _{c=1}^K \left(\sum _{b=1}^K m[b]^2\right)\right)$$ or $$\sum _{j=0}^{n-1} \left(\sum _{c=1}^K \text{$ n$}[c]\right)$$ where $m[b]$ and $n[c]$ ...
user avatar
  • 115
3 votes
1 answer
115 views

An unclear Mathematica result for Borel summation

Summation of divergent series is applied in dynamical systems, q-difference equations, and mathematical physics nowadays (for example, see that book for info), this is not an old-fashioned topic. ...
user avatar
  • 17.2k
6 votes
1 answer
106 views

User plug-in methods for SumConvergence

@Валерий Заподовников remarks: BTW, it is also quite bad that Mathematica does not have Bertrand test. Is there a way to extend the convergence tests in ...
user avatar
  • 216k
1 vote
0 answers
126 views

What's the command for high approximation up to 50 digits?

I am trying to find the numerical value of $\displaystyle \sum_{n=1}^\infty \frac{e^{-n^2/\pi^2}}{n^2}$ up to 50 digits. I used ...
user avatar
5 votes
1 answer
379 views

Fast double sum involving Kronecker symbol

I have three lists $$A=\{\alpha_1...\alpha_N\}$$ $$B=\{\beta_1...\beta_N\}$$ $$M=\{M_1....M_N\}$$ In practice $\alpha_i$ and $\beta_i$ are complex numbers with modulus smaller than 1. The $M_i$s are ...
user avatar
  • 912
0 votes
1 answer
74 views

Parallelize for loop in mathematica

I have the following code which essentially consists of a first for loop that iterates through a very large number of rows and a small for loop that iterates through a small number of columns. The ...
user avatar
  • 111
2 votes
4 answers
203 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: ...
user avatar
0 votes
1 answer
37 views

How to calculate cumulative density from a dynamical output?

I am running a simulation. I want to calculate the cumulate density of each species "C" and "R" from 0 to 100 [I just need the final number, not a graph]. Here is a sample equation ...
user avatar
4 votes
2 answers
163 views

Error animating a 3d parametric plot of a sum

I am trying to animate a sum together with a circle (specifically the vector field $(r \sin \theta , r \cos \theta, u(r,t))$ using Animate and ...
user avatar
5 votes
4 answers
299 views

Sum of new values

So I have the following formula I have found out that c={0.308573, 0.404507, 0.356427, 0.652755, 0.402941} I was just wondering if there is a easier way of ...
user avatar
0 votes
0 answers
68 views

Is it possible to get a step by step to a Sum of a sequence?

$$ \sum_{n=1}^{\infty} \frac{(-1)^n} {n^2} = -\frac{\pi^2}{12} $$ WolframAlpha["Sum[(-1)^n/n^2,{n,1,Infinity}]"] is not working in this case. The version ...
user avatar
  • 1,601
3 votes
1 answer
45 views

Trying to add up values into a matrix

first post here. I'm currently completely stuck and frustrated with mathematica. In retrospective, it might had been a mistake to use it for this, I'm actually considering to somehow export the ...
user avatar
  • 33
5 votes
2 answers
143 views

how to avoid duplication with 2D Sum [closed]

I would like to do 2D $\sum_{i,j}$ where $i\neq j$ and only $(i,j)$ must included and avoiding $(j,i)$ due to symmetry. Here as an example: ...
user avatar
-1 votes
2 answers
76 views

How to use FindSequenceFunction to obtain the general expression of Fourier series?

I want to get cosine series of the following functions. $f(x)=\left\{\begin{array}{cc}\cos x, & 0 \leqslant x<\frac{\pi}{2} \\ 0, & \frac{\pi}{2} \leqslant x \leqslant \pi\end{array}\right.$...
user avatar
  • 1,365
4 votes
1 answer
101 views

How to calculate the sum of the series of Hermite polynomial?

I want to calculate the infinite sum of Hermite polynomials, which works fine with older versions of Mathematica, but with version 13 it doesn't. The infinite sum is: ...
user avatar
  • 43
3 votes
1 answer
114 views

How to use SumConvergence to judge whether this series is convergent?

$\sum_{n=1}^{\infty}\left(\frac{b}{a_{n}}\right)^{n}$ where Limit $\left[a_{n}, n \rightarrow\right.$ Infinity $]=a$, and $a>0 \& \& b>0 \& \& a_{n}>0 $ No results can be ...
user avatar
  • 1,365
4 votes
3 answers
678 views

How can I calculate the sum of this series?

Backslide introduced after 9.0.1, persisting through 13.0. How can I calculate the sum of this series? $\sum_{n=1}^{\infty} \ln \left(1+\frac{1}{n^{2}}\right)$ The sum of this series has been proved ...
user avatar
  • 1,365
0 votes
1 answer
62 views

Adding every entry of two tables

I have to randomly create a polymer (random angle between parts), change a random angle by a bit (delta), and determine the energy difference. RandomAngle contains all the angles and DeltaTable ...
user avatar
0 votes
4 answers
71 views

How to sum over a two tensor with a simple constraint of the form $i<j$?

I am trying to write a sum of the form $$\sum_{i<j}f_{ij}$$ where $i,j\in \{1,2,3,4\}.$ I want to write something like Sum[f[[i,j]], {j,1,4},{i,1,j}] but then ...
user avatar
  • 91
2 votes
1 answer
65 views

Performing sparse sum on Mathematica

I want to evaluate a sum in Mathematica of the form ...
user avatar
-1 votes
1 answer
52 views

what is the Mathematica command for the Euler numbers $E_k?$ [closed]

We know that the Euler numbers $(E_r)$ has many integral and series representations but I am wondering if there is a simpler Mathematica command.
user avatar
0 votes
1 answer
60 views

Double Sum, taking a constant out of the first sum gives a different result

I have a code with the following double sum: Sum[Sum[(-1-k+f[k]) (-l+n+f[l]), {l,k+1,n}], {k,1,n}] /. f[r_] -> If[r == 1, n, 0] With that, I get: I wanted to ...
user avatar
4 votes
1 answer
75 views

Implementing summation under combinatorial restriction

For $m,n\in\mathbb N$, I am interested in the numerical evaluation of $$f(m,n) = \sum_{s_j\in\{\pm1\}}' \prod_{k=1}^{2n-1} (1-e^{\frac{2i\pi}{m} s_k(s_{k+1}+s_{k+2}+\cdots+s_{2n})}),$$ where the ...
user avatar
0 votes
1 answer
77 views

Can i get the right indexes in a sum?

Do have here 4 examples of sums. What to fill in for x and y to get a general true statement ? Can MMA assist me to get these answers for x and y? Sum 1 : $\sum _{k=1}^{n+1} a_k=\sum _{k=1}^n a_k+a_X$ ...
user avatar
  • 649
2 votes
1 answer
148 views

A closed form for a summation to find?

I start as introduction with the well known formula for summing up natural numbers $\sum _{k=1}^n k$= $\frac{1}{2} n (n+1)$ : formula from Gauss proving this by induction $\sum _{k=1}^{n+1} k=\sum _{k=...
user avatar
  • 649
3 votes
2 answers
90 views

How do I prevent Sum indices from being "absorbed" by other sums?

Consider the following test definition: a[j_] = Sum[1/f[(i+j)^2], {i, 1, Infinity}] Now, consider the following expressions: ...
user avatar
3 votes
1 answer
74 views

Is there any particularity of Sum/Product in replacement

Here is an simple replacement: Log[x[k]] /. Log[a_] -> a*xbar I get the answer in my mind: xbar x[k] Similarly, I use ...
user avatar
  • 31
2 votes
1 answer
147 views

Evaluation of a summation involving hypergeometric functions

I need help in evaluating the following tricky summation mainly involving a product of two Kummer's confluent hypergeometric function, ${}_1 F_1(a;b;z)$. Is there some identity of ${}_1 F_1(a;b;z)$ ...
user avatar
0 votes
0 answers
48 views

Adding three list element wise

I want to add n list element wise. ...
user avatar
5 votes
1 answer
132 views

How to speed up this code with DensityPlot and Table?

I need to obtain a matrix and DensityPlot it, then perform a SingularValueList on a 200*200 matrix. But my code is slow, more than 50 seconds. I need the running time to be less than 10 seconds, ...
user avatar
  • 699
0 votes
0 answers
43 views

Are these 3 divergent integrals regularization methods equivalent?

I implemented in Mathematica 3 methods for regularizing divergent integrals, and wonder if they are equivalent. Code: ...
user avatar
  • 2,811
1 vote
1 answer
140 views

How can I get mathematica to prove $\sum_{k=0}^{n-1}\tan\left(\theta+\frac{k\pi}{n}\right)=−n\cot\left(\frac{n\pi}{2}+n\theta\right)$?

How can I get Mathematica to prove $\sum_{k=0}^{n-1}\tan\left(\theta+\frac{k\pi}{n}\right)=−n\cot\left(\frac{n\pi}{2}+n\theta\right)$ (1)? ...
user avatar
  • 325
3 votes
2 answers
130 views

How to integrate a symbolic sum?

I'm trying to integrate a function that involves a finite sum: $$\int_{-\infty}^{\infty}\sum_{j=1}^n (e^{-b t^2}r_j) \,dt$$ I think it should be possible to take the exponent outside the sum: $$\int_{-...
user avatar
  • 131
0 votes
1 answer
70 views

Series development of laurent in a defined domain

I am trying to correct some bills for laurent series with mathematica, but the output I am getting at the moment is not the best. For example, I have this function $$\frac{1}{z^2 + 9}$$ to develop at ...
user avatar
  • 121
4 votes
3 answers
550 views

Infinite sum bug

Why: Limit[Sum[Sqrt[-i^2 + n^2]/n^2, {i, 1, n}], n -> Infinity] (* 0 *) but: Integrate[Sqrt[1 - x^2], {x, 0, 1}] (* Pi/4 *) ...
user avatar
  • 1,365
4 votes
1 answer
161 views

Sum of list elements in a range

I have a list, for example: data = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}; and I wanted to sum every element in range of five, i. e ranges ...
user avatar
0 votes
3 answers
94 views

How can I represent a series with a summary?

As the title suggests, I'm trying to represent a series through a simple summation. For example, the function Series[Exp[x], {x, 0, 10}] obviously gives me the ...
user avatar
  • 121
6 votes
4 answers
350 views

Sum over two independent variables [closed]

I have a function f[x,y] and try to generate a sum of it where x and y vary predictably but ...
user avatar
  • 163
0 votes
1 answer
42 views

Dynamic multiple ordered nested sum

I have a function f[r,n] dependening on two tables $r=\{r_1,...,r_j\},n=\{n_1,...,n_j\}$ which have the same variable size $j$. For given $j$ and given $R$ I want to sum f[r,n] over the range $0< ...
user avatar
0 votes
1 answer
85 views

Conditional summation in mathematica

How to write following conditional sum? $F(\theta1,\theta2)=\sum_{m1,m2} a^*_{m1}a_{m2} A_{m2,m1}(\theta1) \exp[i(m1-m2)\theta2]$, where $A_{m2,m1}(\theta1)$ is a conditional function, such that $A_{...
user avatar
  • 3
4 votes
1 answer
157 views

Evaluation of formula reduces domain and FullSimplify is wrong

I would like a closed form for the formula Sum[Binomial[k - b, n] Binomial[n + b, a], {n, 0, k}] where variables k, a, b are ...
user avatar
0 votes
0 answers
129 views

Fully expanding and distributing a symbolic sum

I have quite a large expression I want to simplify. For example, this can be generated by a recursive definition: ...
user avatar
0 votes
0 answers
34 views

Calculation of integral involving Sum

My code is the following: ...
user avatar
  • 39
0 votes
1 answer
168 views

Computing an infinite sum

I wish to compute $$\sum_{n=1}^{\infty} f(n)e^{-nz}$$ where $f(n)= |\{(a,b,c)| abc=n\}|$ and $z>0$. Its easy to compute that if $n = \prod p_{i}^{\alpha_i}$ where $p_i$ are distinct primes then $$f(...
user avatar
  • 101
3 votes
2 answers
97 views

Faster way to compute a sum within a sum?

I would like a time efficient way to calculate a sum of the following form: ...
user avatar
  • 45
0 votes
1 answer
90 views

Simplifying multiplies of sums into a single double sum

I have the following expression: Sum[x^n, {n, 1, Infinity}]*Sum[Log[m, x], {m, 2, Infinity}] How can I Force Mathematica to write this expression in the following ...
user avatar
  • 350
1 vote
1 answer
84 views

I need to speed up this summation

I tried solving this problem on my own but I cant find a proper solution. I need to evaluate the following equation: $\sum\limits_{m=1\\m\neq i}^n{\left(\dfrac{v_m~(\lambda_i\cdot B-A)~u_i}{(\lambda_m-...
user avatar
7 votes
1 answer
348 views

Help with Double Sum (lattice sum) over all integers m,n of 1/(a+m^2+n^2)

Im researching electric fields in periodic arrays of charges, and encountered this summation that I can't find any published work on. Has anybody encountered a solution to $\sum_{m,n=-\infty,\infty}\...
user avatar

1
2 3 4 5
18