Timeline for An example of a series that is not differentially algebraic?
Current License: CC BY-SA 2.5
8 events
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| Apr 14, 2010 at 20:38 | comment | added | Vladimir Dotsenko | Ah okay, so the property of Gamma that is crucial is that for $g(t)=Gamma'(t)/Gamma(t)$ satisfies $g(t+1)-g(t)=h(t)$ where $h$ is a rational function (some additional properties $h$ has to have are in the paper, just wanted to extract a highlight). | |
| Apr 14, 2010 at 20:27 | comment | added | Gjergji Zaimi | For the gamma function, you can check out fe.math.kobe-u.ac.jp/FE/Free/vol19/fe19-1-7.pdf | |
| Apr 14, 2010 at 11:29 | comment | added | Vladimir Dotsenko | I updated the original question with an additional one motivated by your first example, and an example from the other comment. Do you by any chance know how the proof for Gamma goes? What intuition of Gamma should one use? | |
| Apr 14, 2010 at 10:55 | comment | added | Gjergji Zaimi | Very true! I realized that I had misread the question, right after I posted that answer. | |
| Apr 14, 2010 at 10:50 | history | edited | Gjergji Zaimi | CC BY-SA 2.5 |
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| Apr 14, 2010 at 10:40 | comment | added | Bugs Bunny | I am sorry but I don't understand. It clearly satisfies $(1/f)^{''}+1/f=0$ which you can multiply by $f^4$ to get a polynomial differential equation. | |
| Apr 14, 2010 at 10:40 | history | edited | Gjergji Zaimi | CC BY-SA 2.5 |
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| Apr 14, 2010 at 10:23 | history | answered | Gjergji Zaimi | CC BY-SA 2.5 |