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 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 ...
- 171
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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 ...
- 3,862
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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 ...
- 1,226
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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 ...
- 1,226
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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}]
...
- 259
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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
...
- 2,409
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Summing solutions of $\tan x = x$
I want to show the following identity:
$$\sum_{n=-\infty}^{+\infty}\frac{1}{x_n^2}=\frac{1}{5},$$
where $x_n$ are the non-zero solutions of $$\tan(x) = x.$$
I know how to prove the correctness of this ...
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Differentiating an inactive indexed sum returns 0 in Wolfram 14.2
I recently encountered unexpected behavior when computing the derivative of an inactive indexed sum in Wolfram 14.2.0. This example is taken directly from the official documentation of ...
- 103
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Absolute sum of the difference between the elements of a set and a constant
I want to program an equation that sums the absolute value of the differences between the elements of a set and a constant divided by the number of elements of the set minus one
As shown in the ...
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list with varying numbers of sublists
I have a long list with sublists. The sublist again has subsublists, for example:
...
- 366
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Indefinite sums over variables
Can Mathematica help me simplify difficult sums over variables? For example, assuming that $j>k+1$, I know that
$\sum_{1\leq i \leq j} x_i - \sum_{1\leq i \leq k} x_i = \sum_{k+1\leq i \leq j} x_i$....
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