科研之友
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摘要
We prove that p = 1 and q = 2 are the best possible parameters in the interval (0, infinity) such that the double inequality (e(p/(x+1)) - e(-p/x))/2p < psi'(x + 1) < (e(q/(x+1)) - e(-q/x))/2q holds for x > 0. As applications, some new approximation algorithms for the circumference ratio pi and Catalan constant G = Sigma(infinity)(n=0) ((-1)(n)/(2n + 1)(2)) are given. Here, psi' is the trigamma function.
