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 Some "Theorem" on the generalized superfunction Leo.W Junior Fellow Posts: 30 Threads: 3 Joined: Apr 2021 09/24/2021, 04:37 PM Having a little tiny break from my tons of homework, I contemplated the very case, $f(z)=z+\Gamma(z)$ (Conjugate to more general case $a\ne0,f_a(z)=z+a\Gamma(z)$) Since $\Gamma(z)$ has no zeros, f has no fixed points. But f is not that like the one already constructed: $z+e^z$ which has a well behaviored fixed point at -infinity. My first attempt is to map the fixed point at $\pm{i}\infty$ to 0, using $T(z)=ln(z)/i,F=T^{-1}fT$. however, F won't have a second derivative at z=0, so I got stuck. How would someone construct the family of superfunctions of this f? This will be challenging. I'd like to invite everyone to discuss this. « Next Oldest | Next Newest »

 Messages In This Thread Some "Theorem" on the generalized superfunction - by Leo.W - 05/03/2021, 05:31 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/04/2021, 02:59 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/04/2021, 03:28 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 05/05/2021, 02:59 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/05/2021, 11:43 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 05/05/2021, 07:53 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/06/2021, 05:37 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 05/06/2021, 06:23 AM RE: Some "Theorem" on the generalized superfunction - by MphLee - 05/06/2021, 11:54 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/06/2021, 09:26 PM RE: Some "Theorem" on the generalized superfunction - by MphLee - 05/06/2021, 10:39 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/07/2021, 06:37 AM RE: Some "Theorem" on the generalized superfunction - by MphLee - 05/07/2021, 09:27 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/07/2021, 11:49 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 05/07/2021, 11:05 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/08/2021, 07:38 AM RE: Some "Theorem" on the generalized superfunction - by MphLee - 05/10/2021, 07:34 PM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 05/08/2021, 07:58 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 05/08/2021, 08:40 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 05/08/2021, 11:45 PM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 05/11/2021, 12:14 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 06/08/2021, 06:44 PM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 06/09/2021, 12:40 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 06/09/2021, 10:10 AM RE: Some "Theorem" on the generalized superfunction - by MphLee - 05/11/2021, 08:41 PM RE: Some "Theorem" on the generalized superfunction - by MphLee - 06/09/2021, 03:00 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 06/09/2021, 06:00 PM RE: Some "Theorem" on the generalized superfunction - by MphLee - 06/09/2021, 11:17 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 08/07/2021, 10:06 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 06/09/2021, 11:48 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 06/25/2021, 09:42 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 08/01/2021, 11:23 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/02/2021, 08:08 PM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/04/2021, 03:58 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 08/05/2021, 04:36 PM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/06/2021, 01:35 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 08/07/2021, 09:13 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/07/2021, 11:45 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/06/2021, 09:22 AM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/08/2021, 11:22 PM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 08/09/2021, 07:12 PM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/10/2021, 04:49 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 08/10/2021, 11:09 PM RE: Some "Theorem" on the generalized superfunction - by JmsNxn - 08/11/2021, 03:08 AM RE: Some "Theorem" on the generalized superfunction - by Leo.W - 09/24/2021, 04:37 PM

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