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本文求出了L2空间权为e-x的Bernstein-Markov不等式的渐进精确常数,即设pn(x)为(0,∞)上次数不超过n的代数多项式,则有∫∞0p12n(x)e-xdx＜[(2/π)2(n+1/2)2+1/4]∫∞0p2n(x)e-xdx且常数"(2/π)2","1/2"和阶"n2"已不可改进.