MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top


I have the following series:

$$ \sum_{n=2}^\infty \frac{t^n}{\Gamma(a n)} = ?,\qquad t\ge 0, $$

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?

Thank you very much for any hints and helps! :-)


share|cite|improve this question
up vote 7 down vote accepted

It's a special case of the Mittag-Leffler function.

share|cite|improve this answer
Thanks Fredrik Johansson. :-) – Anand Feb 16 '12 at 12:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.