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

I'm curious: Is there any ideas about how a closed form or even a series formula, recurrence, etc. could be found for the Taylor coefficients of the tetrational function at 0 developed from, e.g. the Abel iteration, or the Cauchy integral (which seem to give the same thing though it's not proven), to base e?


and what is ? We have and then , etc. but is there any way that coefficient for example could be expressed in terms of elementary or "well-known" (used by the general maths. community, that is -- e.g. gamma, polylog, zeta, erf, etc.) non-elementary special functions and known mathematical constants (like e, pi, eulergamma, etc.)? Even if it can only be done with an infinite expansion like an infinite sum or something involving those? Or is this function simply so darned exotic that it will utterly refuse and defy any and all attempts to try to relate it to known mathematical functions? Smile

Messages In This Thread
Coefficients of Tetrational Function - by mike3 - 03/28/2010, 03:25 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  New mathematical object - hyperanalytic function arybnikov 4 1,065 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 674 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 1,128 10/22/2018, 11:29 AM
Last Post: Xorter
  Taylor polynomial. System of equations for the coefficients. marraco 17 18,241 08/23/2016, 11:25 AM
Last Post: Gottfried
  Should tetration be a multivalued function? marraco 17 18,697 01/14/2016, 04:24 AM
Last Post: marraco
  Introducing new special function : Lambert_t(z,r) tommy1729 2 4,020 01/10/2016, 06:14 PM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 2,182 04/21/2015, 01:02 PM
Last Post: tommy1729
  The inverse gamma function. tommy1729 3 8,211 05/13/2014, 02:18 PM
Last Post: JmsNxn
  entire function close to sexp ?? tommy1729 8 10,376 04/30/2014, 03:49 PM
Last Post: JmsNxn
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 7,548 07/17/2013, 09:46 AM
Last Post: Gottfried

Users browsing this thread: 1 Guest(s)