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 Mittag-Leffler series for generating continuum sum? mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 12/13/2009, 02:48 AM (This post was last modified: 12/13/2009, 02:53 AM by mike3.) (12/12/2009, 09:53 PM)bo198214 Wrote: 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). I.e. given two transseries representations for an analytic function, if both converge and so do their Faulhaber continuum sums, do those sums agree whenever both converge? It would be interesting to determine this, but I'm not sure what the proof would be like. Another thing I've wondered about is, could there be some way to assign some sort of value to the divergent sums of Faulhaber coefficients given an arbitrary power series of nonzero convergence radius as input? Failing the Faulhaber method, could there be some other way to define continuum sum that agrees with it but covers a lot more ground? « 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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