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 Mittag-Leffler series for generating continuum sum? bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 12/11/2009, 11:16 AM (This post was last modified: 12/11/2009, 11:18 AM by bo198214.) So I had a look at E. Borel: Leçons sur les séries divergentes (1901) In chapter V, page 156 he explains the Mittag-Leffler expansion. Mostly I fighted my way through the text with an online translator. I found the following interesting formulas, where $\phi$ is the function we search the expansion of: $g_n(x)=\sum_{\lambda_1=0}^{n^{2n}}\sum_{\lambda_2=0}^{n^{2n-2}} \dots\sum_{\lambda_n=0}^{n^2} \frac{\phi^{(\lambda_1+\dots+\lambda_n)}(0)}{\lambda_1!\dots\lambda_n!} \left(\frac{x}{n}\right)^{\lambda_1+\dots+\lambda_n}$ $G_0(x)=g_0(x)=\phi(0)$ $G_n(x)=g_n(x)-g_{n-1}(x)$ for $n>0$, $\phi(x)=\sum_{n=0}^\infty G_n(x)$ « 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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