Hello, id like to find the analytic expression for the following sum.

Sum[Exp[-Sqrt[x]], {x, 1, infinity} ]

I can prove convergence, but i cant figure out a way to find the sum, i have tried maths programs (Maple, Mathematica), books on integrals (Gradshteyn, Prudnikov) and tried myself with no result so far.

Thanks for the Help in advance!