Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hello,

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! :-)

Anand

share|improve this question
add comment

1 Answer

up vote 7 down vote accepted

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

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

Your Answer

 
discard

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.