Timeline for Sum of subset of geometric series: a^2^n
Current License: CC BY-SA 2.5
8 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 11, 2010 at 21:37 | comment | added | Kevin O'Bryant | Okay, now I see that the question includes $0<a<1$. | |
| May 11, 2010 at 21:37 | comment | added | Kevin O'Bryant | Well, it motivates the nonexistence of an algebraic formula valid over the complexes. There are other "closed expressions" that may qualify, particularly if Henry isn't thinking of this as a complex power series. For example, if the coefficients are in the binary field $F_2$, then the series is algebraic. | |
| May 11, 2010 at 3:25 | vote | accept | Henry Yuen | ||
| May 11, 2010 at 3:17 | vote | accept | Henry Yuen | ||
| May 11, 2010 at 3:25 | |||||
| May 11, 2010 at 3:10 | comment | added | Wadim Zudilin | Agreed. My point is that Mahler's series are already special functions (as far as I know $f(z)$ does not satisfy an algebraic differential equation but only the functional equation relating $f(z^d)$ to $f(z)$). | |
| May 11, 2010 at 3:01 | comment | added | Qiaochu Yuan | I think a simpler motivation is that the function has a natural boundary. Anything one might naively call an elementary function won't. | |
| May 11, 2010 at 2:55 | history | answered | Wadim Zudilin | CC BY-SA 2.5 |