Generalized recursive operators

[Ivars]

=...=0,007297583=1/137,0316766

I'm not sure, it seems like no one has mentioned that this value is also the ratio between the action potentials of (electron/photon), better known as the "fine structure constant", also known as alpha. However, your sum is only accurate to 4 decimal places, which is still better than the previous approximation of 1/137, which is only accurate to 3 decimal places. Good job.

Andrew Robbins

Hi, Andy,

Thanks. Of course I was aiming for fine structure constant, assumed everyone would notice- I live in assumptions, sometimes.

I do not know how accurate are the assymptotic values You and JFox and GFR have derived. I they are accurate to enough decimal places, than this indeed is rather accurate SIMPLE symbolic approximation of fine structure constant (I mean You can always approximate any number using arbitrary values and constants,or infinite sums ) - I used only 5 terms, integer coefficients, integer powers , simple logic how they change, and the value of pentatition asymptote which must be a true mathematical constant. Perhaps this can be even written down as simple formula , just need a Symbol for the asymptote value.

From my point of view, hyperoperations are exactly the place to look for alpha value. And having 5 terms in a 5-tation sum also seemed a nice fit.

I would expect this formula is somehow extendable giving even better fit with either higher hyperoperations, or involving hyperoperations in formula itself, but for that there is a need to understand what does this pentation asymptote might mean, physically. Which is why I started to draw spirals, so far for me it remains unresolved issue.

Ivars