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 Mittag-Leffler series for generating continuum sum? bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 12/12/2009, 09:53 PM (12/12/2009, 08:18 PM)mike3 Wrote: *sighs* I guess its back the drawing board, then. This continuum sum thing seems really difficult to generalize to arbitrary analytic functions, as is needed for tetration. Well, even if there was a simple Mittag-Leffler expansion, the chance to have luck with a convergent Faulhaber application, was anyway quite low, wasnt it? If not even entire the continuum sum of exp(exp(x)) was convergent. Hm, so summarizing: exp(x) has a convergent Faulhaber sum. non-entire functions have no convergent Faulhaber sum. functions with over-exponential growth (like exp(exp(x))) have probably no convergent Faulhaber sum. However if there was a way to rearrange the terms, there might convergence be possible (as you greatly showed with exp(exp(x)) and 1/(x+1)). But then my question would be whether the value depends on how the terms are rearranged (I mean not only giving different branches, but a continuum of solutions). « Next Oldest | Next Newest »

 Messages In This Thread Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 09:14 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/14/2009, 04:54 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 08:24 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 09:18 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/14/2009, 10:05 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 10:24 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/17/2009, 03:21 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/17/2009, 12:10 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/17/2009, 06:54 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/17/2009, 08:44 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/17/2009, 09:20 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/17/2009, 11:22 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/18/2009, 08:05 AM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/18/2009, 09:55 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/18/2009, 10:43 AM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/18/2009, 11:01 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/28/2009, 10:36 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/28/2009, 10:56 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/29/2009, 03:48 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 12/11/2009, 11:16 AM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/11/2009, 11:45 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 12/12/2009, 01:47 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/12/2009, 08:18 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 12/12/2009, 09:53 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/13/2009, 02:48 AM Mittag-Leffler product ? Ramanujan's master theorem - by tommy1729 - 12/13/2009, 05:41 PM RE: Mittag-Leffler product ? Ramanujan's master theorem - by mike3 - 12/13/2009, 08:19 PM RE: Mittag-Leffler product ? Ramanujan's master theorem - by tommy1729 - 12/13/2009, 11:15 PM RE: Mittag-Leffler product ? Ramanujan's master theorem - by mike3 - 12/14/2009, 04:40 AM

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