08/13/2022, 06:51 PM
(This post was last modified: 08/13/2022, 06:56 PM by marcokrt.
Edit Reason: Adding LaTeX tags
)
Very interesting, thank you!
Recently, I posted another (and maybe easier) question on the same line that I would like to be answered: convergence value of this series.
I suspect that the constant above could be very close to \( e^{\frac{1}{e}} \), but I cannot find the exact value... it would be interesting since it compares (asymptotically) a unitary increment on hyper-2 to a unitary increment on hyper-4.
Recently, I posted another (and maybe easier) question on the same line that I would like to be answered: convergence value of this series.
I suspect that the constant above could be very close to \( e^{\frac{1}{e}} \), but I cannot find the exact value... it would be interesting since it compares (asymptotically) a unitary increment on hyper-2 to a unitary increment on hyper-4.
For every radix \(r\geq 2\), the congruence speed of tetration stabilizes at a positive constant for all bases \(a>1\) with \(\mathrm{rad}(r )\nmid a\) if and only if \(r\) is squarefree. (NNTDM 32(3), Appendix B)