含有Wallis比的一个正项级数

A Positive Series Involving the Wallis Ratio

考虑了正项级数∑n=0 ∞[1·3…(2n-1)/2·4…(2n)]^(8)证明了当s≤2时,级数发散;当s>2时,级数收敛.当s=3时,证明了级数的和为[Г(1/4)]^(4)/(4π^(3)).也给出了该级数的几个注记.

This paper considers the positive series ∑n=0 ∞[1·3…(2n-1)/2·4…(2n)]^(8) We prove that the series diverges for 5<2,and converges for s>2.When 5=3,we give the sum of the series.Also,we give several remarks of the series.