An inequality involving the gamma and digamma functions

• Autorzy: Qi F. , Guo B.-N.

Identyfikatory

DOI

10.1515/jaa-2016-0005

• Języki publikacji: EN

Abstrakty

EN

In the paper, the authors establish an inequality involving the gamma and digamma functions and apply it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.

Słowa kluczowe

EN

gamma function; psi function; polygamma function; inequality; negativity; monotonicity; application

PL

funkcja gamma; funkcja psi; funkcja polygamma; nierówność; negatywność; monotoniczność

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2016
• Tom: Vol. 22, nr 1
• Strony: 49--54
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Qi F.

• Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, P. R. China
• College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, 028043, P. R. China
• Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300387, P. R. China

autor

Guo B.-N.

• School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, P. R. China

Bibliografia

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• [3] N. Elezović and J. Pecarić, Differential and integral f-means and applications to digamma function, Math, Inequal. Appl. 3 (2000), no. 2,189-196.
• [4] B.-N. Guo and F. Qi, Two new proofs of the complete monotonicity of a function involving the psi function, Bull. Korean Math. Soc. 47 (2010), no. 1,103-111.
• [5] B.-N. Guo and F. Qi, Sharp inequalities for the psi function and harmonic numbers, Analysis (Berlin) 34 (2014), no. 2, 201-208.
• [6] S. Guo, F. Qi and H. M. Srivastava, Necessary and sufficient conditions for two classes of functions to be logarithmically completely monotonic, Integral Transforms Spec. Funct. 18 (2007), no. 11,819-826.
• [7] B.-N. Guo, F. Qi, J.-L. Zhao and Q.-M. Luo, Sharp inequalities for polygamma functions, Math. Slovaca 65 (2015), no. 1, 103-120.
• [8] J.-C. Kuang, Changyông Bùdëngshî (in Chinese), Appl. Inequal., 3rd ed., Shandong Science and Technology Press, Ji'nan City, 2004.
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• [17] F. QÎ, S. Guo and B.-N. Guo, Complete monotonicity of some functions involving polygamma functions, J. Comput. Appl. Math. 233 (2010), no. 9, 2149-2160.
• [18] F. Qiand W.-H. Li, A logarithmically completely monotonic function involving the ratio of gamma functions, J. Appl. Anal. Comput. 5 (2015), no. 4, 626-634.
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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.