与$\zeta(2k 1)$函数有关的两类快速收敛级数

Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.

New Rapidly Convergent Series Concerning $\zeta(2k 1)$

Values of new series $$\sum_{n=1}^{\infty}\frac{(2n-1)!\zeta(2n)}{(2n+2k)!}\alpha^{2n},\ \ \sum_{n=1}^{\infty}\frac{(2n-1)!\zeta(2n)}{(2n+2k+1)!}\beta^{2n}$$ are given concerning $\zeta(2k+1)$, where $k$ is a positive integer, $\alpha$ can be taken as $1$, $1/2$, $1/3$, $2/3$, $1/4$, $3/4$, $1/6$, $5/6$ and $\beta$ can be taken as $1$, $1/2$. Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for $\alpha = 1/3$, or $\alpha = 1/4$, or $\alpha = 1/6$.