Hi! I've stumbled upon a convergent sum of the form:

This sum converges for every with . I've checked properties of the function numerically (for real values of ) and found that for close to zero the function goes approximately as . I need to find an expression for the function for close to 1. I've already found that it goes as , where and is another function that goes to some finite constant of approximately 0.89 as goes to 1. I'd be happy if anyone knows an analytic expression of the function (exact or approximate for close to 1).

Thanks in advance.

/Simon