I'm new to Mathematica. I'm trying to find a result in terms of $a$ and $c$ for the following summation with the restrictions declared in the code below:
Assuming[a > 0 && -1 < c < 0, Sum[Exp[-a*Sqrt[i + c]]/Sqrt[i + c], {i, 1, ∞}]]
Though this is a convergent series, the above yields no result; it gives an output like the following:
$\qquad \displaystyle\sum_{i=1}^{\infty}{\frac{e^{-a\sqrt{c+i}}}{\sqrt{c+i}}}$
Even Simplify does not work!
Apart from Mathematica, does anyone have any idea how I can analytically obtain a closed form expression for the above summation?
I will be really grateful if somebody can help with my problem.