Approximation of 1/x by exponential sums in [1, ∞)

Approximations of 1/x by sums of exponentials are well studied for finite intervals. Here the error decreases like 𝒪(exp(−ck)) with the order k of the exponential sum. In this paper we investigate approximations of 1/x in the interval [1, ∞). We prove estimates of the error by and confirm this asymptotic estimate by numerical results. Numerical results lead to the conjecture that the constant in the exponent equals .