(10/11/2010, 11:46 PM)mike3 Wrote: Consider . If we apply Mueller's formula to this at the real axis we get a reals-only continuum sum that is not analytic anywhere, heck, it may not even be real-differentiable anywhere(!).

Why do you think this function should have good, analytic, differentiable continuous sum? I think it should not regardles of the method used. It is really bad function for continuous summation.