Linked Questions
10 questions linked to/from Limit of partial sums involving inverse squares
216 votes
26 answers
19k views
What are some useful, undocumented Mathematica functions?
There have already been some questions about some undocumented functionality in Mathematica. Such as (please add to these lists!) How can one find undocumented options or option values in Mathematica?...
14 votes
7 answers
3k views
Numerical evaluation of a sum
I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often it'...
12 votes
5 answers
599 views
Possible bug in finite sum over inverse squares $\sum\limits_{i=1}^n \frac{1}{(x (n-i)+i)^2}$
Revisiting the problem Limit of partial sums involving inverse squares I found another difficulty with Sum[] Consider this sum ...
8 votes
3 answers
660 views
How to find a more precise value of integral?
Mathematica 11 produces ...
11 votes
3 answers
383 views
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 ...
16 votes
1 answer
792 views
What happened to SequenceLimit?
In older versions of Mathematica, there was a function called SequenceLimit that allowed taking the limit of a numerical sequence. It is useful for speeding up the ...
4 votes
3 answers
2k views
How to integrate a function which is only known at discrete points?
I have an integration to do. I want to integrate $$ \int_0^\infty \sin^2(2\pi t)f(t)\mathrm{d}t $$ where $f(t)$ is known only at discrete values given in an array in the form $\{t_i,f_i\}$ with $i=1\...
2 votes
2 answers
308 views
How to numerically check the binoharmonic series?
$$ \sum _{k=1}^{\infty }\frac{4^kH_{2k}^2}{k^2\binom{2k}{k}}=8G^2+\frac{103}{2}\zeta \left(4\right)-22\operatorname{Li}_4\left(\frac{1}{2}\right)+7\ln ^2\left(2\right)\zeta \left(2\right)-\frac{11}{12}...
3 votes
0 answers
691 views
Epsilon algorithm to accelerate sum's convergence in a functional approach
I am trying to learn to use Mathematica in an efficient way. Thus, I decided to spend some time on functional programming. I would like to implement the so-called epsilon algorithm, that is used to ...
0 votes
1 answer
94 views
How can I solve this limit? [closed]
How can I solve this limit? thanks you!!!