All Questions
3
questions
-2
votes
1
answer
103
views
How to find the approximate value of $\operatorname{arcosh}$?
Does anyone knows a good way to approximate $\operatorname{arcosh}$ between $1.0$ and $1.1$ precisely? Me and some others are using the standard series $$\ln(2x)-\sum_{n=1}^\infty\left(\frac{(2n)!}{2^{...
- 203
3
votes
1
answer
262
views
On $\mathrm{\sum_{x\in\Bbb Z}sech(x)=3.142242…}$
Inspired by
This question,
I started to wonder about simpler series. I have seen similar questions to the following, but none had this special case explicitly. It is related to the q-digamma ...
- 12.5k
11
votes
2
answers
268
views
Calculate the sum: $\sum_{x=2}^\infty (x^2 \operatorname{arcoth}(x) \operatorname{arccot} (x) -1)$
$${\color\green{\sum_{x=2}^\infty (x^2 \operatorname{arcoth} (x) \operatorname{arccot} (x) -1)}}$$
This is an impressive sum that has bothered me for a while. Here are the major points behind the sum.....
user266519