论文标题
基本和普通伽马功能的完全单调比率
Completely monotonic ratios of basic and ordinary gamma functions
论文作者
论文摘要
我们研究了伽马和Q-gamma函数的乘积比的对数完全单调性的条件，这些函数的参数是该变量的线性函数。在Q情况下某个明确书面度量的非负性和经典Q = 1的某个基本功能的某些明确书面措施的非负性方面，我们提供了必要和充分的条件。在后一种情况下，我们进一步提供了简单的新足够条件，从而导致许多对数完全单调伽马比的新示例。最后，我们将一些结果应用于研究某些伽马比和合理功能的单调性。
We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of a certain explicitly written measure in the q case and of a certain elementary function in the classical q=1 case. In the latter case we further provide simple new sufficient conditions leading to many new examples of logarithmically completely monotonic gamma ratios. Finally, we apply some of our results to study monotonicity of some gamma ratios and rational functions.
