Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
1,027 questions
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Summation contains additional $\frac{\zeta(3)}{8\pi^2}$ term if evaluated without presimplification
As noted in this math.se question from 2018 (which was using WolframAlpha and Mathematica 7.0, though it persists in 14.0.0), Mathematica's evaluation of the following sum depends on where the ...
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How can I include all terms within a sum? [duplicate]
I would like to include terms that factorize a sum within the sum.
For instance, from
k Sum[Subscript[x, i], {i, 1, L}]
getting
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how to remove the divergent term from the summation?
I am doing the summation over two indices: m and n
Suppose I want to remove those terms from the summation which has m==n, what ...
- 167k
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How to Force the PolyGamma[0, x] function or the HarmonicNumber[ x ] function
I'm crunching some infinite summations, and sometimes Mathematica generates results that have the PolyGamma[0, x] function (which is the Digamma) and sometimes the <...
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Summation question?
I have following summation that I want to implement using Mathematica:
...
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Problem with extracting a constant multiplier out of sum
For a generic symbol A[i]
2 Sum[A[i], {i, 1, n}] == Sum[2 A[i], {i, 1, n}]
does not return ...
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Double Sum Computation Issue
I'm trying to compute a double sum...
For scalars, it seems to be working fine. Here is an example:
...
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How to output results of the sum, $\sum_{a=1}^2\sum_{b=1}^a\sum_{c=1}^b 2^a3^b 5^c$ into a list (table)?
I'm trying to write a code that can approximate the following formula,
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{A}$$
In this M.SE question I was convinced that $(\...
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How to output each summand of $\sum_{n=1}^k \frac1n$ into a list?
From real analysis, I'm trying to learn more about this famous equation in this post of Mathematics.SE:
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{1}$$
I won't ask ...
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No method can regularize the sum Sum[k^3*Exp[k], {k, 0, ∞}]
When entering
Sum[k^3*Exp[k], {k, 0, ∞},Regularization->"Dirichlet"]
Mathematica returns the expression unevaluated. But other regularization methods ...
- 167k
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How to define a function through a summation of other functions efficiently?
I want to plot the following function:
$F(x, \omega) = \sum_{m = - \infty}^{\infty}\sum_{n = 1}^{\infty} \theta(\omega m - \xi_{mn}) \cos(x \xi_{mn})$
Where $\xi_{mn}$ is defined as the BesselJZero[m,...
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Sum of combination of elements of a matrix
Give a $N \times N$ matrix $M$ in MMA, I am interested in finding a very particular sum using its matrix elements:
$ \sum_{i \neq j \neq k \neq l}^{N} M_{ij}M_{jk}M_{kl}M_{li}$,
which is of some use ...
- 113k
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Efficient nested summation with matrices
Consider a case where I have an array a[i,j]. Each of these a[i,j]consists of a $2 \times 2$ matrix. I would like to compute the ...
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Annoying issue with infinite summation
I want to evaluate a larger number of terms with infinite summations.
For example, there appear summations like
Sum[HarmonicNumber[j]^2/j^4, {j, 1, Infinity}]
...
- 156k
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Wrong result from `Sum` applied to `Sinc`
I want Wolfram to calculate a closed form for the sum
s = Sum[Sinc[Pi*(n - i)], {i, 1, n}]
It's happy to oblige, and produces the answer
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