Approximation of 1 / x by Exponential Sums in [ 1 , ∞ )
نویسنده
چکیده
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 on the interval [1,∞). We prove estimates of the error by O(exp(−c√k)) and confirm this asymptotic estimate by numerical results. Numerical results lead to the conjecture that the constant in the exponent equals c = π √ 2. AMS Subject Classification: 11L07, 41A30, 41A50
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تاریخ انتشار 2005