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Tagged with experimental-mathematics sequences-and-series
3 questions
15
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Does anyone remember what happened to the experimental search for polynomial identities for $\pi$?
So a while back I was on the internet and had encountered a website containing an experimental search for identities for $\pi$. My memory was that the page belonged to either Jonathan Sondow or ...
- 2,689
2
votes
2
answers
655
views
Expansion of inverse logarithmic integral in terms of lambert w
Cipolla and Césaro both gave expansions of $\operatorname{li}^{-1}$ in tems of nested $\log$ functions. I think it can be written in terms of the Lambert-W function in the form:
$\operatorname{li}^{-...
- 1,903
1
vote
1
answer
427
views
When does this limiting ratio give a real root $x$ to the equation of the form $\sum\limits_{k=0}^d \frac{x^k a_{k+1}}{k!}=0$?
By searching the Inverse Symbolic Calculator, we appear to be able to make the following conjecture about a real root to the equation:
$$\sum\limits_{k=0}^d \frac{x^k a_{k+1}}{k!}=0 \tag{1}$$
Let the ...
- 1,183