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seen Sep 30 '13 at 13:46

Sep
5
comment Upper bound for an infinite series with a square root
That's great, thanks. I'd come across an integral version before (Gradshteyn and Ryzhik, 12.411), but hadn't realised it was generalisable in this way. I come from an engineering background, so my knowledge of the connections between these things is sometimes a bit limited.
Sep
5
comment Upper bound for an infinite series with a square root
That's an excellent result. I had suspected the solution (on a hunch), but I couldn't think of how to show it. Also, I've never come across the series form of Jensen's inequality before, so thanks for that too.
Sep
5
awarded  Supporter
Sep
5
accepted Upper bound for an infinite series with a square root
Sep
4
revised Upper bound for an infinite series with a square root
Fixed the inequality so that it works for $k \geq 0$ rather than just $k > 0$ (the range wasn't specified previously).
Sep
4
asked Upper bound for an infinite series with a square root
Dec
21
revised Sum of an infinite series with regularized gamma functions
Edited to make the dependency of the inner series on the index of the outer series explicit.
Dec
21
comment Sum of an infinite series with regularized gamma functions
Thanks, Johnny! I'll persevere...
Dec
20
awarded  Commentator
Dec
20
comment Sum of an infinite series with regularized gamma functions
For example, if you expand my original expression, you get: $$S = e^{-x-y} \left(x + \frac{x^2}{2} (1 + y) + \frac{x^3}{6}(1 + y + \frac{y^2}{2}) + \cdots + \frac{x^n}{n!}(1 + y + \cdots + \frac{y^{n - 1}}{(n-1)!}) + \cdots \right)$$
Dec
20
awarded  Cleanup
Dec
20
comment Sum of an infinite series with regularized gamma functions
EDIT: I've reverted your edit of my question to the original.
Dec
20
revised Sum of an infinite series with regularized gamma functions
rolled back to a previous revision
Dec
20
comment Sum of an infinite series with regularized gamma functions
Thanks again, but I think you might misunderstand what I wrote. The expression I want to evaluate is exactly as I wrote earlier. You can't simply replace the outer series with the lower regularized Gamma function, and the inner one with the upper regularized Gamma function, because the upper limit of the inner series has a dependency on the index of the outer one. It's not simply the product of two separable functions.
Dec
20
comment Sum of an infinite series with regularized gamma functions
Yes, the outer series is indexed by $k$, which ranges from $1$ to $\infty$, but the inner series is indexed by $l$, which ranges from $0$ to $k - 1$.
Dec
20
comment Sum of an infinite series with regularized gamma functions
Thanks, but I think you missed the dependency of the second series on $k$, i.e. $\sum_{l=0}^{k-1} \cdots$.
Dec
20
accepted Advice on an integral involving the error function
Dec
20
revised Sum of an infinite series with regularized gamma functions
The outer series should start at k = 1, not k = 0.
Dec
20
asked Sum of an infinite series with regularized gamma functions
Dec
10
awarded  Teacher