About one series. Are there some related special functions? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T07:22:46Z http://mathoverflow.net/feeds/question/88612 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88612/about-one-series-are-there-some-related-special-functions About one series. Are there some related special functions? Anand 2012-02-16T09:06:26Z 2012-02-16T10:29:31Z <p>Hello,</p> <p>I have the following series:</p> <p>$$\sum_{n=2}^\infty \frac{t^n}{\Gamma(a n)} = ?,\qquad t\ge 0,$$</p> <p>where the parameter $a\in (0,1]$, $\Gamma$ is the Gamma function. When $a=1$, the above sum gives $t(e^t-1)$. When $a=1/2$, it gives $e^{t^2}t^2 (1+ Erf(t))$ where $Erf(\cdot)$ is the standard error function. It is not difficult to see that it indeed converges. For general $a\in (0,1]$, are there some special functions related to this sum?</p> <p>Thank you very much for any hints and helps! :-)</p> <p>Anand</p> http://mathoverflow.net/questions/88612/about-one-series-are-there-some-related-special-functions/88616#88616 Answer by Fredrik Johansson for About one series. Are there some related special functions? Fredrik Johansson 2012-02-16T09:27:08Z 2012-02-16T09:27:08Z <p>It's a special case of the <a href="http://en.wikipedia.org/wiki/Mittag-Leffler_function" rel="nofollow">Mittag-Leffler function</a>.</p>