Road testing Ansus' continuum product formula

[mike3]

The fact is that during the calculation I never applied the sum to a function with limited radius of convergence. At first iteration - to x+1 function, at the second iteration - to the erfi(x). Both have infinite convergence radius. The vertical asymptote emerges only after infinite number of iterations. At any iteration the approximating function has no asymptote.

So you were iterating it symbolically, in which case power series considerations would not apply. But I'm sure at some point the symbolic iteration would have no closed form (run out of special functions), and so could not continue past that point. So to use the formula for more accuracy and at all sorts of bases (incl. the fabled b = 0.04 and other bases between 0 and \( e^{-e} \)) would require an extension of continuum sum that could work on something like a powerseries or similar.