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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1answer
20 views

using a list of parameters in NSum

I am trying to make a function that uses NSum, that takes a list of parameters. But NSum doesn't appear to play nicely with lists. A minimum working example is: ...
4
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2answers
151 views

How to get the right approximation for a series involving the harmonic number?

The right numerical value of the closed form of $\sum_{n=1}^\infty\frac{4^n H_n^2}{{2n\choose n}n^2}$ is $40.66752074791188333...$. I tried to verify this result on Mathematica using the command: <...
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0answers
73 views

Computation of infinite series containing Zeta function

(this is my first question on this forum I'm totally inexperienced in mathematica) Consider the given alternating series: $$f(x) =\sum_{n=0}^\infty \frac{2a_n(x-1)^{2n+1}}{\zeta(-2n-1)}$$ Here, $a_n= (...
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21 views

How to assign a summation to existing formula derived from elsewhere? [closed]

I derived an equation algebraically and the solution is in the form of test1=a*z[t]/(a+x[i]^2+y[i]^2)^(2/7) To continue to build up the equation, I have to assign ...
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0answers
33 views

Confuse about joining and totaling sets with different lengths [closed]

Here is my code: ...
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1answer
66 views

How would I graph this function on Mathematica?

I could graph 1/n^2, but I don't understand how to graph the fractional part (x).
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1answer
81 views

Does Mathematica have a problem with sums involving Stirling numbers of the second kind?

In one of my calculations, I run the command: Sum[(StirlingS2[k - 1, 4] + StirlingS2[k, 4])/6^k, {k, Infinity}] Surprisingly, ...
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0answers
42 views

Evaluation of a double summation invovlving hypergeometric and exponential functions

I am trying to compute the following double summation over the indices, $m$ and $n$, which involves the hypergeometric function, ${}_2 F_1$, an exponential function and, factorials as a part of a ...
1
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1answer
129 views

How does Mathematica evaluate these sum and integral?

How does Mathematica internally evaluate the following (interrelated) sum and integral, and how does it do the subsequent simplification? (I mean, based on what mathematical facts?) ...
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1answer
26 views

How do I plot various values of the partial sums for a function with 2 variables?

This is what I have tried so far. I have a function defined as the below: ...
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0answers
22 views

Why summation of matrices in the MatrixForm gives wrong result? (an example is given) [duplicate]

I want to calculate the sum of two matrices, doing that in MatrixForm, I get which is wrong, but writing them as ...
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2answers
41 views

How to collect coefficients that has summation in ODE

I have the following equation, equation= x''[t]+a*x'[t]+b*x[t]+c*y[t]+d*u[t]+e*v[t]+Sum[f[i]*x[t]+g[i]*u[t]+h[i],{i,1,n}]+k When I collect the coefficient of each ...
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0answers
71 views

How to sum the KroneckerDelta[] in equation?

How to sum the KroneckerDeltas in following equation? k, p1, ...
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1answer
59 views

Understanding a “strange” output about a finite sum

Input: Sum[HarmonicNumber[k]/k^2, {k, 1, m}] That is $$\sum_{k = 1}^{m} \frac{H_k}{k^2}$$ Output I will attach a screenshot for I don't even know how to write ...
2
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1answer
40 views

Exponents manipulation

When I type(a^2)^s Mathematica does not give me $a^{2s}$ instead it gives ${(a^2)}^s$. Is there a way to make it print $a^{2s}$. It made some real difference where ...
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2answers
108 views

Implementing a formula from a paper

Is this:Table[Exp[-((1250^2) dism11[[n, m]])/Sum[dism11[[i, j]], {i, n, 1250}, {j, m, 1250}]], {n, 1, 1250}, {m,1, 1250}] a correct way to implement: I am kinda ...
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2answers
121 views

Exploring Matrix Powers with Wolfram (using Sum Notation)

I am trying to gain an intuition for what algebraically happens to a square matrix (say a $2$-dimensional square matrix) when it is successively multiplied by itself. I have used ...
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2answers
84 views

Does this sum converge, and why?

Mathematica says the following sum Sum[(mm Gamma[mm])/ Gamma[-(1/2) + mm] - (mm^(3/2) - (3 Sqrt[mm])/8 - (7 Sqrt[1/mm])/ 128), {mm, 1, \[Infinity]}] ...
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1answer
66 views

How can I calculate the Allan Variance of a list of Data?

I have a list with over 10.000 elements of data. Now I wanna calculate the Allan Variance of this Measurement. The Allan Variance is defined as following: $$\sigma_y^2(\tau)=\frac1{2\tau^2}\langle(x_{...
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48 views

Equations with Tensor product and Ket in Mathematica:

I tried to express this equation in Mathematica: I defined necessary things: ...
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2answers
81 views

Mathematica ruins domain after explicit summation?

I'm working with this function ...
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1answer
79 views

speed up symbolic summation

I have the following summation L=24; sind=Range[-Pi,Pi,2*Pi/L]; Sum[f, {x, sind}, {y, sind}, {x1, sind}, {y1, sind}, {x2, sind}, {y2, sind}] where ...
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1answer
28 views

Expand product of symbolic sums (with identically named indices)

I have an expression that is a product of two symbolic sums. Sum[a[k], {k, 1, n}]*Sum[b[k], {k, 1, n}] How can I expand this expression? I want to see something ...
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4answers
222 views

Trouble with the numerical evaluation of a series

The series is $\;S=\displaystyle{\sum_{n=0}^\infty 2^{-n+\sin(n\pi/5)}}$. Mathematica doesn't find a closed form for Sum[2^(-n + Sin[n Pi/5]), {n, 0, Infinity}], so ...
3
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2answers
237 views

How to calculate this summation

η = 0.05211184484645051`; Sum[η/(r + 1) + ArcTan[η/(r + 1)] $r$ start from $0$. How to calculate this summation until it becomes less than 10^-5?
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0answers
103 views

Sum cause a Recursion problem

Sum[((-1)^(i + 1)*Binomial[n, i]*(n - i)!)/n!, {i, 1, n}] This cause a Recursion problem. As the comment said, If simplify the formula and then sum it, problem ...
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1answer
59 views

simplifying indefinite sums containing Kronecker Deltas

I want to simplify indefinite sums containing KroneckerDeltas, e.g: $\sum_{k,k1,q} \beta(q) \beta(k+k1+q) \delta(k1+q)= \sum_{k,q} \beta(k)\beta(q)$ where $k,k1,q \;\epsilon \; \mathrm{R}$ ...
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0answers
29 views

summation involving Kronecker Deltas

I see that: Sum[u[q] u[k] v[k1] v[k + k1 + q] KroneckerDelta[k1 - q], {k1, -\[Infinity], \[Infinity]}] produces the correct result: ...
2
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1answer
61 views

Numerical sum optimization

I need to compute the following sum as fast as possible: $$P_{ijkl}=\sum_{p,q,r,s}^nW_{sqpr}H_{js}G_{rl}A_{ipkq}$$ I came up with this code: ...
8
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2answers
370 views

Cannot reproduce well-known summation result

Bug introduced in 4.2 or 5.0, persisting through 12.2.0. Note: this is a repost of my OP on math.SE. I am posting it here because multiple users with different Mathematica versions have given me the ...
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4answers
65 views

Periodical sum of rows by a certain step

I've been struggling with one problem. I have a classic matrix in this example 12x4 such as: matrix = Table[i, {i, 12}, {4}] ...
3
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2answers
76 views

Vectorization of multifold summation to speedup

I searched this website but didn't find any suitable answer describing how one can speed up summation in Mathematica using vectorization techniques and other techniques. I often have to numerically ...
-1
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1answer
61 views

Why can't Mathematica confirm this simple identity? [closed]

It is well known that for positive integer $n\geq2$, $$ \sum_{k=1}^{n-1} \frac{(-1)^{k-1}(k-1)!^2}{(n^2-1^2)\ldots(n^2-k^2)}=\frac{1}{n^2}-\frac{2(-1)^{n-1}}{n^2 \binom{2n}{n}}. $$ This identity ...
3
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1answer
111 views

Infinite summation giving weird results

We are searching in our group for closed forms of derivatives of hypergeometric functions. This leads to expressions like $\sum\limits_{m=2}^\infty \frac{z^m\Gamma[m-1/2]H_m}{2m^2\sqrt{\pi}\Gamma[m]}$ ...
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2answers
367 views

Faster, More Elegant Way to Produce a Recursive Sequence of Rational Numbers [closed]

I am studying a recursion below: $$B_{N,0}=1$$ $$B_{N,k}=-\binom{N+k}{k}^{-1}\sum_{j=0}^{k-1}\binom{N+k}{j}B_{N,j}$$ Now I'm not great at writing in Mathematica. It's been a while since I've used it. ...
0
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1answer
86 views

$\sum_{n=1}^{+\infty}\frac{\cos(\frac{n\pi}{2})}{n}$ gives wrong answer in Mathematica? [closed]

I wanted to compute $\sum_{n=1}^{+\infty}\frac{\cos(\frac{n\pi}{2})}{n}$ on Mathematica and it says the sum does not converge, even though it does by Dirichlet's test. When I plugged the same sum in ...
0
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1answer
63 views

Analytical expression for a limit

I have the following equation $$\Delta v = -g I_\mathrm{SP} \left( 1 + \frac{1}{24} \frac{\mu}{r^3} \frac{g^2 {I_\mathrm{SP}}^2}{T^2} \frac{{m_p}^2}{n^2} \right) ^{-1} \sum _{k=1} ^n \log \left( \...
2
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0answers
56 views

Evaluate fractional derivative

I needed to evaluate the following fractional derivative of $f(t) = e^{t^2}$. The fractional derivative that I'm currently studying is the Grunwald-Letnikov fractional derivative, which is defined as ...
2
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4answers
190 views

Usage of 'Less than' condition in Sum

I have following sum: $$ \sum_{\substack{n,j\\j<n}}^{3} x_nx_j$$. How can I give this $j<n$ condition in Sum?
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0answers
30 views

Calculating a sum that's taken over all of the k-element subspaces of an n-element space

Currently I constructed a formula (the idea from which it arose was completely combinatorial, won't bother you with that) and was wondering whether this is applic-able in Mathematica (I've used it so ...
0
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2answers
35 views

Plotting partial sum with complex number

$$\sum_{n=1}^{N} e^{2\pi in\sqrt2}$$ We have to use Accumulate and ListLinePlot, and my implementation so far with upper bound ...
0
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1answer
82 views

Difficulty plotting sum of functions

I'm interested in plotting this function (provided in equation 11 of this paper): $$ \begin{aligned} \begin{aligned} S_{S}(\omega)=& \sum_{m_{5}, m_{I}, m_{S}^{\prime}, m_{I}^{\prime}=-\infty}^{\...
3
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4answers
392 views

How to find the sum of that series related to Legendre functions of the second kind?

I mean $$\sum _{n=0}^{\infty } \frac{Q_n\left(\frac{\sqrt{2}}{2}\right)}{n+1}. $$ It's unclear to me whether the series under consideration converges. I have strong doubts concerning its closed form. ...
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2answers
56 views

How to make calculations involving symbolic summation?

I want to minimize a function involving the sum of $n$ fixed (but indetermined) $x$ values, for example: Minimize[Sum[(x[i] - a)^2, {i, 1, n}], a] Expected answer: ...
3
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0answers
62 views

Algorithm used by Mathematica for evaluating partial sums

Today, while using mathematica, I entered the command Sum[1/Factorial[n], {n, 0, x}] and found that: $$\sum_{x\geq n\geq0}\frac{1}{n!}=\frac{e\Gamma(x+1,1)}{\Gamma(...
1
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0answers
35 views

Sum over certain indices not working

Define a function $h$ by h[m_,n_]:=2^n Binomial[m,Ceiling[m/2]]Binomial[n,Ceiling[n/2]]Ceiling[m/2]Ceiling[n/2](m-1)b^(m+n)/((m+n)m!n!) I am trying to evaluate <...
4
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3answers
128 views

The symbolic result does not give a proper answer when inputs are specified

Define F by F[m_, k_, i_, j_] := (-1)^(m+k)/(m!*k!)*2^m*Binomial[m, i]*Binomial[k+1,j] I am trying to find this sum: ...
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1answer
23 views

Binomial sum only expanded, not computed [closed]

I want to compute this sum: $\sum _{n=1}^4 \frac{(2 n-1) \sum _{k=0}^{n-1} \text{Binom}(6,k) \text{Binom}(10,-k+2 n-1)}{\text{Binom}(16,2 n-1)}$ ...
1
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2answers
71 views

To write mathematica code for summation using a given data

I am given a set like some terms from the partition of $20$: $\{\{17, 3\}, \{13, 7\}, \{11, 3, 3, 3\}, \{7, 7, 3, 3\}, \{7, 5, 5, 3\}, \{5, 5, 5, 5\}\}$. From the above data, $20= \underline{1}*17+\...
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2answers
53 views

Computing the coefficients of series

I am trying to fully expand the following $$\sum_{n=0}^{\infty} \frac{q^{\frac{n(n+1)}{2}}}{(q;q)_n}$$ Which when expressed in Mathematic is: q^(n*(n + 1)/2)/QPochhammer[q, q, n] I would like to be ...

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