【摘要】 利用Γ函数的对数微商的渐近公式,我们建立了下面双边不等式:12n+∑2p+1k=1(-1)kBk2kn2k<∑nk=11k-lnn-γ<12n+∑2pk=1(-1)kBk2kn2k,这里γ=0.57721566…是Euler常数,Bk(k=1,2,…)是Bernoulli数,p0和n1是整数.更多还原

【Abstract】 By using the asymptotic formula of the logarithmic derivative of the gamma function, we establish the following double inequality:12n+∑2p+1k=1(-1) kB_k2kn 2k<∑nk=11k-ln n-γ<12n+∑2pk=1(-1) kB_k2kn 2k,where γ=0.57721566…denotes Euler′s constant, B_k (k=1,2,…)are Bernoulli mumbers, and p0and n1are integers.更多还原