Alternate continuum sum formula?

[mike3]

And how does this relate to the integral+contiuum-sum formula you gave earlier? And it would not seem convergent for, e.g. \( b > e^{1/e} \) or \( 0 < b < 1 \).

Yes. But I do not know what inverse function expansion converges for \( b > e^{1/e} \).

Wouldn't the integral+continuum-sum thing you gave before converge for those? Because \( \frac{1}{D_x \mathrm{tet}_b(x)} \) rapidly goes to zero as \( x \rightarrow \infty \) for such bases.