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 An explicit series for the tetration of a complex height Vladimir Reshetnikov Junior Fellow Posts: 12 Threads: 3 Joined: Dec 2011 01/14/2017, 09:09 PM (This post was last modified: 01/15/2017, 11:38 PM by Vladimir Reshetnikov.) By the way, in the well-known representation of the tetration as an exponential series ${^z a} = \sum_{m=0}^{\infty} \; c_m q^{mz},$ the coefficients have a q-binomial representation $c_m=\sum_{n=m}^\infty \sum_{k=0}^{n}(-1)^{m+n+k} \; q^{\binom{n-k}{2} + \binom{m}{2}-m(n-1)}\;\frac{\binom{n}{m}_q\;\binom{n}{k}_q}{(q; \; q)_n}\;({^k a})$ The coefficients also satisfy the recurrence $c_m=\frac{\log(a)}{m\left(1-q^{1-m}\right)}\sum_{k=1}^{m-1}kq^{-k}c_{k}c_{m-k},\;\;m>1$ « Next Oldest | Next Newest »

 Messages In This Thread An explicit series for the tetration of a complex height - by Vladimir Reshetnikov - 10/22/2016, 10:29 PM RE: An explicit series for the tetration of a complex height - by sheldonison - 10/23/2016, 02:50 PM RE: An explicit series for the tetration of a complex height - by Gottfried - 10/26/2016, 01:55 AM RE: An explicit series for the tetration of a complex height - by Vladimir Reshetnikov - 01/11/2017, 12:02 AM RE: An explicit series for the tetration of a complex height - by JmsNxn - 01/12/2017, 04:45 AM RE: An explicit series for the tetration of a complex height - by Vladimir Reshetnikov - 01/12/2017, 11:55 PM RE: An explicit series for the tetration of a complex height - by JmsNxn - 01/13/2017, 12:46 AM RE: An explicit series for the tetration of a complex height - by Vladimir Reshetnikov - 01/13/2017, 01:12 AM RE: An explicit series for the tetration of a complex height - by JmsNxn - 01/13/2017, 07:47 PM RE: An explicit series for the tetration of a complex height - by Vladimir Reshetnikov - 01/13/2017, 08:30 PM RE: An explicit series for the tetration of a complex height - by JmsNxn - 01/14/2017, 12:36 AM RE: An explicit series for the tetration of a complex height - by Vladimir Reshetnikov - 01/14/2017, 02:13 AM RE: An explicit series for the tetration of a complex height - by JmsNxn - 01/14/2017, 02:48 AM RE: An explicit series for the tetration of a complex height - by Vladimir Reshetnikov - 01/14/2017, 09:09 PM

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