# 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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### 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. ...
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....
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1 vote
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### 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 $n[c]$ ...
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### 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. ...
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### 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 ...
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1 vote
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### 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 ...
• 435
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### 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 ...
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### 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 ...
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### 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: ...
• 435
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### 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 ...
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### 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 ...
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 ...
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 ...
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### 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 ...
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### 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: ...
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### How to use FindSequenceFunction to obtain the general expression of Fourier series?

I want to get cosine series of the following functions. $f(x)=\left\{\begin{array}{cc}\cos x, & 0 \leqslant x<\frac{\pi}{2} \\ 0, & \frac{\pi}{2} \leqslant x \leqslant \pi\end{array}\right.$...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Performing sparse sum on Mathematica

I want to evaluate a sum in Mathematica of the form ...
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.
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### 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 ...
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### 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 ...
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### 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 : $\sum _{k=1}^{n+1} a_k=\sum _{k=1}^n a_k+a_X$ ...
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