摘要
The authors prove that for arbitrarily given b is an element of (0, infinity) r is an element of (0, 1) and n is an element of N-0, and for lambda is an element of R, the functions @@@ a bar right arrow F(a,b; a + b; r/a(lambda) and a bar right arrow F(a, b; a + b; r) - Sigma(n)(k=0) (a,k)(b,k)/(a+b,k)k! r(k)/a(lambda) @@@ are both strictly increasing (decreasing) on (0, infinity) if and only lambda <= 0 (lambda >= max{1, b}, respectively), where F (a, b; a + b; r) denotes the Gaussian hypergeometric function. This result gives one answer to an open problem raised by Qiu et al.
- 单位