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 Generalized phi(s,a,b,c) JmsNxn Long Time Fellow Posts: 571 Threads: 95 Joined: Dec 2010 02/08/2021, 12:30 AM (This post was last modified: 02/08/2021, 12:32 AM by JmsNxn.) (02/07/2021, 05:03 PM)tommy1729 Wrote: .... Analytic continuations are perhaps not possible for your case (or my analogue) in attempt to go from Re(a) < 0 to Re(a) > 0 or vice versa. In fact there is a huge gap in my understanding about continuations for infinite compositions. Or Riemann surfaces of infinite compositions. But I think a natural boundary occurs for Re(a) = 0 in both our cases. .... tommy1729 Yes, I'd have to agree with you as it being a natural boundary. When we flip to $\Re(a) < 0$ all we get is the equation, $ \psi(s-1,a,b,c) = e^{as + b + c \psi(s,a,b,c)}$ From, $ \psi(s,a,b,c) = \Omega_{j=1}^\infty e^{a(s+j) + b + cz}\bullet z = \phi(-s,-a,b,c)\\$ « Next Oldest | Next Newest »

 Messages In This Thread Generalized phi(s,a,b,c) - by tommy1729 - 02/04/2021, 01:17 PM RE: Generalized phi(s,a,b,c) - by MphLee - 02/04/2021, 06:25 PM RE: Generalized phi(s,a,b,c) - by tommy1729 - 02/05/2021, 12:59 AM RE: Generalized phi(s,a,b,c) - by JmsNxn - 02/06/2021, 12:18 AM RE: Generalized phi(s,a,b,c) - by tommy1729 - 02/07/2021, 05:03 PM RE: Generalized phi(s,a,b,c) - by JmsNxn - 02/08/2021, 12:30 AM RE: Generalized phi(s,a,b,c) - by tommy1729 - 02/07/2021, 05:37 PM

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