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+--- Thread: [MSE] Mick's function (/showthread.php?tid=1724)
[MSE] Mick's function - Caleb - 03/08/2023
See Mick's interesting function here:
https://math.stackexchange.com/questions/4654387/analytic-continuation-of-a-lambert-series-fz-sum-n-1-infty-frac2n-zn
This is a nice function to consisider in the process of beginning to extend the definition of summing beyond natural boundary. Here, we can't quite just plug in on the outside, but there's a way to extend it in a pretty similar way to the other approachs. Does this function satisfy f(x) = f(1/x)? What about other things? It woudl be interesting to check out how nature of the extension of this function beyond its natural boundary.
RE: [MSE] Mick's function - Caleb - 03/08/2023
Damn this is a beautiful function-- I really should be getting work done now-- so I'm not going to give too much info. But, here are some plots-- I simply can't resist at least graphing it! Also, normally I would upload the images somewhere so I can embedd them here, but I'm short on time so here is a google drive link: https://drive.google.com/drive/folders/1ALx4eiktgpefz-uZsQqN-OiCi_3dQ6eW?usp=share_link