Inequalities for the gamma function

Archiv der Mathematik

Volumn 91, Issue 6, 2008, Pages 554-563

  Batir, Necdet ^a  

^a YUZUNCU YIL UNIVERSITY   (Turkey)

Author keywords

Burnside's formula; Complete monotonicity; Digamma function; Gamma function; Harmonic numbers and inequalities; Polygamma functions; Stirling formula

Indexed keywords

EID: 58149116525     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00013-008-2856-9     Document Type: Article

References (25)

1. H. ALZER, Gamma function inequalities, Numer. Algor., DOI10.1007/511075-008-9160-4, 2008.
2. H. ALZER AND N. BATIR, Monotonicty properties of the gamma function, Appl. Math. Lett. 20, 778-781 (2007).
3. H. ALZER, Inequalities for the gamma function, Proc. Amer. Math. Soc. 128, 141-147 (1999).
4. H. ALZER AND A. Z. GRINSHPAN, Inequalities for the gamma, and q-gamma functions, J. Approx. Theory 144, 67-83 (2007).
5. H. ALZER., AND C. BERG, Some classes of completely monotonie functions II, The Ramanujan J. 11, 225-248 (2006).
6. H. ALZER, On Ramanujan's double inequality for the gamma function, Bull. London Math. Soc. 35, 601-607 (2003).
7. H. ALZER, On some inequalities for the gamma and psi functions, Math. Comp. 66, no. 217, 373-389 (1997).
8. G. D. ANDERSON, et al., Inequalities for zero-balanced hypergeometric functions, Trans Amer. Math. Soc. 347, 1713-1723 (1995).
9. G. ANDREWS, R. ASKEY, AND R. ROY, Special functions, Encyclopedia of Mathematics and Its Applications, 71, Cambridge University Press, 1999.
10. N. BATIR, Sharp inequalities for factorial n, Proyecciones 27, 97-102 (2008).
11. N. BATIR, On some properties of the gamma function, Expo. Math. 26, 187-196 (2008).
12. N. BATIR, Some new inequalities for gamma and polygamma functions, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), Article 103, 9 pp.
13. C. BERG AND G. FORST, Potential theory on locally compact abelian groups, Ergeb. Math. Grenzgeb. 87 Springer-Verlag, Berlin, 1975.
14. L. BONDESSON, Generalized gamma convulation and related classes of distributions and densities, Lecture Notes in Statistics, 76, Springer-Verlag, New York, 1992.
15. W. BURNSIDE, A rapidly convergent series for log N!, Messenger Math. 46, 157-159 (1917).
16. W. A. DAY, On monotonicities of the relaxation functions of viscoclastic material, Proc. Cambridge Philos. Soc. 67, 503-508 (1970).
17. N. ELEZOVIC, C. GIORDANO, AND J. PECARIC, The best bounds in Gautschi's inequality, Math. Inequal. Appl. 3, 239-252 (2000).
18. W. FELLER, An introduction to probability theory and its applications, v.2, Willey, New York, 1984.
19. L. FRENZEN, Error bounds for asyptotic expansions of the ratio of two gamma functions, SIAM J. Math. Anal. 18, 890-896 (1987).
20. A. Z. GRINSHPAN AND M. E. H. ISMAIL, Completely monotonie functions involving the gamma and g-gamma functions, Proc. Amer. Math. Soc. 134, 1153-1160 (2006).
21. C. H. KIBERLING, A probabilistic interpretation of complete monotonicity, Aequationes Math. 10, 152-164 (1974).
22. S. L. QIU, AND M. VUORINEN, Some properties of the gamma and psi functions, with applications, Math. Comp. 74, no. 250, 723-742 (2005).
23. G. K. SRINIVASAN, The gamma function: An Eclectic Tour, Amer. Math. Monthly 114, 297-315 (2007).
24. H. M. SRIVASTAVA AND J. CHOI, Series associated with the zeta and related functions, Kluwer, Boston, 2001.
25. D. V. WIDDER, The Laplace Transform, 1981.