二类涉及Riemann zeta函数的积分值

Two Integrals Value Involving Riemann Zeta Function

利用伯塔函数的性质,得到了二类积分W(m,k)=integral ((logmtlogk(1-t))/(1-t))dt from n=0 to 1和U(2m,k)=integral θ2mlogk(2cos(θ/2))dθ from n=0 to 1的递推公式,其值涉及Riemann zeta函数,结果的计算可以通过计算机实现,其中m和k为正整数.

This paper contains two integrals formula, given as follows,W（m,k）=integral （（logmtlogk（1-t））/（1-t））dt from n=0 to 1 and U（2m,k）=integral θ2mlogk（2cos（θ/2））dθ from n=0 to 1The equation is derived based on the properties of beta function, whose values refer to Riemann zeta function. The results also can be obtained by computer implementaion, where m and k are positive integers.