Timeline for Elementary functions with zeros only at the positive integers
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2010 at 1:51 | comment | added | Dylan Thurston | Sorry, I just reread the question and saw "meromorphic", which changes things. | |
| May 9, 2010 at 1:50 | comment | added | Dylan Thurston | This is, however, the "most elementary" function with this property, for some reasonable notions of elementary (at least, assuming you want simple zeroes). For instance, any other function with the same zeroes has larger asymptotic growth; this is a version of the Hadamard Factorization Theorem. More precisely, if $f(z)$ has simple zeroes at the positive integers, then there is a polynomial $g(z)$ so that $f(z) = e^{g(z)}/\Gamma(1-z)$. So if you don't think the gamma function is elementary, the answer to your original question is "no". | |
| May 8, 2010 at 18:46 | comment | added | Fredrik Johansson | The gamma function is not elementary. | |
| May 8, 2010 at 18:45 | history | answered | Dylan Thurston | CC BY-SA 2.5 |