Complete monotonicity of some functions involving polygamma functions

Authors:
Feng Qi;Senlin Guo;Bai-Ni Guo
Affiliations:
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300160, China;Department of Mathematics, Zhongyuan University of Technology, Zhengzhou City, Henan Province, 450007, China;Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300160, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In the present paper, we establish necessary and sufficient conditions for the functions x^@a|@j^(^i^)(x+@b)| and @a|@j^(^i^)(x+@b)|-x|@j^(^i^+^1^)(x+@b)| respectively to be monotonic and completely monotonic on (0,~), where i@?N, @a0 and @b=0 are scalars, and @j^(^i^)(x) are polygamma functions.