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COMPLETELY MONOTONIC FUNCTIONS RELATING TO THE GAMMA AND PSI FUNCTIONS

X. Li
장전수학회 (Jangjeon Mathematical Society)|2009.06|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제12권 제1호|pp. 51-55|DOI 10.17777/pjms.2009.12.1.008

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참고문헌

키워드

Gamma functioncompletely monotonic functioninequality.
주제분류수학

초록

In this paper, the complete monotonicity of the function x 7↔ ψ(x+1)- ψ (ax+1)+ln a on (0,∞) for a > 0 and the logarithmically complete monotonicity of the function x ↔Γ(x + 1)a/Γ(ax + 1) on (0,∞) for a > 0 are considered and the corresponding results by C. Alsina and M. S. Tomas, J. Sandor are extended.

Abstract

In this paper, the complete monotonicity of the function x 7↔ ψ(x+1)- ψ (ax+1)+ln a on (0,∞) for a > 0 and the logarithmically complete monotonicity of the function x ↔Γ(x + 1)a/Γ(ax + 1) on (0,∞) for a > 0 are considered and the corresponding results by C. Alsina and M. S. Tomas, J. Sandor are extended.

참고문헌 (20)

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