Hi James -
this seems really great what, and how, you're explaining/discussing that things. Even it takes me in derivations, which I'd always avoided due to lack of original/basic insight (my formal math-edication has been limited to linear algebra, while I completely missed any progress in the analysis-course, for students of "general informatik" in the early 1970ies). But how you expose consideration & arguing is really a delight, and perhaps I'll find the energy to step into it even deeper. Unfortunately since my retiring two years ago my mental energy for those things degrades already and I think I'll have to accept, that not many new things shall get entry in my mind... But really, your style of discourse is attractive again.
I had tried to step into this fractional calculus some years ago, did some exercises, but when it came to the "half-derivative of zeta at zero" I gave up (even had tried to get help on this in MSE; that has been 7 years ago, I've been much fitter...). I'll surely read your answer again with hope to be able to catch up some more insight, let's see. And nice to see, that one gets up this explorative adventure with the "uncompleting the gamma" with a qualified access at all. <heart-warming> ... :-)
At the moment I'm absorbed with the other problem (discussing x --> x-1/x) and properties of periodic points im comparision with what I've learned about periodic points of the exp(z) function, and writing up an essay on my explorations and discoveries. The occuring problem to make a vision of a continuous iteration for instance through a 3-periodic set in the exp(z) compared with a 3-periodic set in the x-->x-1/x problem is absorbing me most massively at the moment.
Just wanted -at least- respond to your engagement timely enough to show that I'm valuating it very much!
Gottfried
this seems really great what, and how, you're explaining/discussing that things. Even it takes me in derivations, which I'd always avoided due to lack of original/basic insight (my formal math-edication has been limited to linear algebra, while I completely missed any progress in the analysis-course, for students of "general informatik" in the early 1970ies). But how you expose consideration & arguing is really a delight, and perhaps I'll find the energy to step into it even deeper. Unfortunately since my retiring two years ago my mental energy for those things degrades already and I think I'll have to accept, that not many new things shall get entry in my mind... But really, your style of discourse is attractive again.
I had tried to step into this fractional calculus some years ago, did some exercises, but when it came to the "half-derivative of zeta at zero" I gave up (even had tried to get help on this in MSE; that has been 7 years ago, I've been much fitter...). I'll surely read your answer again with hope to be able to catch up some more insight, let's see. And nice to see, that one gets up this explorative adventure with the "uncompleting the gamma" with a qualified access at all. <heart-warming> ... :-)
At the moment I'm absorbed with the other problem (discussing x --> x-1/x) and properties of periodic points im comparision with what I've learned about periodic points of the exp(z) function, and writing up an essay on my explorations and discoveries. The occuring problem to make a vision of a continuous iteration for instance through a 3-periodic set in the exp(z) compared with a 3-periodic set in the x-->x-1/x problem is absorbing me most massively at the moment.
Just wanted -at least- respond to your engagement timely enough to show that I'm valuating it very much!
Gottfried
Gottfried Helms, Kassel