一些不等式限定了q函数的某些比值

Mohammed Hashimu
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引用次数: 0

摘要

在这篇简短的文章中,我们建立了经典Gamma函数的一些著名不等式的q-类似物和一些限定比值Γ_q (x)/Γ_q (y)的不等式,其中Γ_q(.)是Gamma函数的q-类似物。给出结果的方法利用了函数的严格对数凸性和经典中值定理,其中涉及psi函数的q-模拟。最后,证明的结果提供了经典伽玛函数的一些已知结果的q-类似。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Some inequalities bounding certain ratios of the q-gamma function
In this short paper, we established q- analogues of some well-known inequalities for the classical Gamma function and some inequalities bounding the ratio Γ_q (x)/Γ_q (y), where Γ_q (.) is the q-analogue of the Gamma function. The method employed in presenting the results made use of strict logarithmic convexity of a function and classical mean value theorem involving the q-analogue of the psi function. At the end, the proven result provided the q-analogue of some known result concerning the classical Gamma function.
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