×

zbMATH — the first resource for mathematics

A class of logarithmically completely monotonic functions related to the gamma function with applications. (English) Zbl 1258.26009
Summary: It is given a necessary and sufficient condition and a necessary condition for a class of functions involving the gamma function to be logarithmically completely monotonic. As applications, inequalities about psi, polygamma functions and ratio of gamma functions are established.

MSC:
26A48 Monotonic functions, generalizations
33B15 Gamma, beta and polygamma functions
26D07 Inequalities involving other types of functions
26D20 Other analytical inequalities
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] DOI: 10.1090/S0025-5718-97-00807-7 · Zbl 0854.33001 · doi:10.1090/S0025-5718-97-00807-7
[2] DOI: 10.2307/2154966 · Zbl 0826.33003 · doi:10.2307/2154966
[3] Atanassov R. D., C. R. Acad. Bulgare Sci. 41 pp 21– (1988)
[4] DOI: 10.1016/j.jmaa.2005.08.056 · Zbl 1099.33002 · doi:10.1016/j.jmaa.2005.08.056
[5] DOI: 10.1080/10652469.2010.483899 · Zbl 1213.33004 · doi:10.1080/10652469.2010.483899
[6] DOI: 10.1080/10652469.2010.538525 · Zbl 1230.33004 · doi:10.1080/10652469.2010.538525
[7] Erdélyi A., Higher Transcendental Functions (1953) · Zbl 0051.30303
[8] DOI: 10.1016/j.cam.2008.04.028 · Zbl 1157.26005 · doi:10.1016/j.cam.2008.04.028
[9] DOI: 10.1016/j.aml.2007.10.028 · Zbl 1202.33002 · doi:10.1016/j.aml.2007.10.028
[10] DOI: 10.1080/10652460701528933 · Zbl 1136.33001 · doi:10.1080/10652460701528933
[11] DOI: 10.1016/j.amc.2007.08.011 · Zbl 1139.33300 · doi:10.1016/j.amc.2007.08.011
[12] DOI: 10.1007/BF00531524 · Zbl 0314.60017 · doi:10.1007/BF00531524
[13] Kečlić J. D., Publ. Inst. Math. (Beograd) (N.S.) 11 pp 107– (1971)
[14] DOI: 10.1016/j.camwa.2004.01.016 · Zbl 1081.33005 · doi:10.1016/j.camwa.2004.01.016
[15] DOI: 10.1080/10652469.2010.535970 · Zbl 1230.33006 · doi:10.1080/10652469.2010.535970
[16] DOI: 10.1080/10652460701358976 · Zbl 1144.26013 · doi:10.1080/10652460701358976
[17] DOI: 10.1155/2010/493058 · Zbl 1194.33005 · doi:10.1155/2010/493058
[18] DOI: 10.1016/j.jmaa.2004.04.026 · Zbl 1046.33001 · doi:10.1016/j.jmaa.2004.04.026
[19] DOI: 10.1016/j.aam.2009.03.003 · Zbl 1179.26036 · doi:10.1016/j.aam.2009.03.003
[20] DOI: 10.1017/S1446788700011393 · Zbl 1094.33002 · doi:10.1017/S1446788700011393
[21] Saigo M., Proc. Amer. Math. Soc. 110 pp 71– (1990)
[22] Wei Y.-J., Adv. Stud. Contemp. Math. 15 pp 253– (2007)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.