Understanding \(f(z,\theta) = e^{e^{i\theta}z}

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Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\)

MphLee Offline

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12/28/2022, 12:42 PM

Excuse me, I hate to be that guy who ask without doing his homework... I don't get you chain of deduction, but I see the final formula and you seems to suggest that it is beautiful and also it is some analogue of Euler equation...

Can you rewrite it in a way, maybe giving a special case, that a noob like me can recognize as analogue of \(e^{ix}=\cos x +i\sin x\) or of \(e^{i\pi}=-1\)?

Also the importance of Euler identity is, secretly, that it defines a surjective group homomorphisms turning the real line into the circle... rolling it up in the unitary complex numbers....

Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)

\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)

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Messages In This Thread

Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 12/10/2022, 04:23 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 12/12/2022, 04:22 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 12/12/2022, 04:51 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 12/22/2022, 07:34 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by MphLee - 12/28/2022, 12:42 PM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 12/30/2022, 02:20 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/01/2023, 04:31 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/01/2023, 05:29 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/03/2023, 04:35 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/03/2023, 10:31 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/06/2023, 06:20 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/06/2023, 08:54 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by MphLee - 01/06/2023, 07:05 PM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/08/2023, 06:19 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/08/2023, 08:17 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by MphLee - 01/08/2023, 11:11 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/08/2023, 12:41 PM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/10/2023, 05:39 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/10/2023, 07:24 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/12/2023, 08:39 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/14/2023, 11:47 PM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/18/2023, 01:36 AM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by tommy1729 - 01/19/2023, 11:25 PM

RE: Understanding \(f(z,\theta) = e^{e^{i\theta}z} - 1\) - by JmsNxn - 01/23/2023, 02:38 AM

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