I agree with everything you're saying, Leo. Very well thought out; I never gave it much thought how to actually numerically calculate this function--but I'm sure it exists. It won't have an asymptotic expansion at zero; just how your noting. What's especially interesting, is that it doesn't even have a formal taylor series at zero; like with sine. I've never given it thought how to evaluate this; I only ever really worried about \( \sin \) when talking about the neutral fixed point theory. It's a good function to keep in mind.
I'll give it some thought; and think if I can create a way of calculating this. I'm still busy trying to make my tetration calculator for the beta method; and that is filling up all my "numerical" thought processes. I still think the fractional calculus approach should work; but you'd need to know the shape of the petals to make it work. Which, I don't have the energy to calculate.
I'll give it some thought, though. Good luck at uni; and I hope the floods don't get you too bad. Don't worry about rushing anything--mathematics is a slow beast. I'm the lucky few where coronavirus has kept me comfy at home--so I got nothing but time to work. Don't burn yourself out. I appreciate your contributions
.
Regards, James.
And for god's sake read John Milnor. His graduate text on complex dynamics is a must read. You're too smart to put that book off. All your questions can be answered by him--and better than I could
I'll give it some thought; and think if I can create a way of calculating this. I'm still busy trying to make my tetration calculator for the beta method; and that is filling up all my "numerical" thought processes. I still think the fractional calculus approach should work; but you'd need to know the shape of the petals to make it work. Which, I don't have the energy to calculate.
I'll give it some thought, though. Good luck at uni; and I hope the floods don't get you too bad. Don't worry about rushing anything--mathematics is a slow beast. I'm the lucky few where coronavirus has kept me comfy at home--so I got nothing but time to work. Don't burn yourself out. I appreciate your contributions
.Regards, James.
And for god's sake read John Milnor. His graduate text on complex dynamics is a must read. You're too smart to put that book off. All your questions can be answered by him--and better than I could