Thread Rating:
• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 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

 Possibly Related Threads... Thread Author Replies Views Last Post Perhaps a new series for log^0.5(x) Gottfried 3 2,656 03/21/2020, 08:28 AM Last Post: Daniel Complex Tetration, to base exp(1/e) Ember Edison 7 6,363 08/14/2019, 09:15 AM Last Post: sheldonison Taylor series of i[x] Xorter 12 18,013 02/20/2018, 09:55 PM Last Post: Xorter Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 2,494 12/26/2016, 03:01 AM Last Post: tommy1729 2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,538 12/21/2016, 01:27 PM Last Post: tommy1729 Taylor series of cheta Xorter 13 19,837 08/28/2016, 08:52 PM Last Post: sheldonison Tetration series for integer exponent. Can you find the pattern? marraco 20 24,167 02/21/2016, 03:27 PM Last Post: marraco [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 54,266 03/27/2015, 11:28 PM Last Post: tommy1729 Explicit formula for the tetration to base $$e^{1/e}$$? mike3 1 4,267 02/13/2015, 02:26 PM Last Post: Gottfried Negative, Fractional, and Complex Hyperoperations KingDevyn 2 8,385 05/30/2014, 08:19 AM Last Post: MphLee

Users browsing this thread: 1 Guest(s)