Some completely monotonic functions involving polygamma functions and an application |
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| Authors: | Feng Qi Run-Qing Cui Bai-Ni Guo |
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| Affiliation: | Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics, Henan Polytechnic University, Jiaozuo City, Henan 454010, China |
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| Abstract: | By using the first Binet's formula the strictly completely monotonic properties of functions involving the psi and polygamma functions are obtained. As direct consequences, two inequalities are proved. As an application, the best lower and upper bounds of the nth harmonic number are established. |
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| Keywords: | Completely monotonic function Gamma function Psi function Polygamma function Harmonic number Harmonic sequence |
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