一个关联特殊函数的Hilbert型不等式

On a Hilbert-type inequality related to special functions

通过引进参数,利用实分析的技巧,建立一个常数因子与Riemann Zeta函数、Gamma函数等特殊函数有关的Hilbert型积分不等式,并给出了其等价形式.作为应用,赋予定理中参数不同的值,给出了一些有意义的特殊结果.

By introducing parameters, and using the method of real analysis, a Hilbert-type integral inequality whose constant factor is related to Riemann Zeta function and Gamma function was established. Moreover, the equivalent form of this inequality was also established. As applications of the conclusion, gave the parameters different values, some meaningful and special results was considered.