A Turán-type inequality for the gamma function

Journal of Mathematical Analysis and Applications

Volumn 350, Issue 1, 2009, Pages 276-282

  Alzer, Horst ^a   Felder, Giovanni ^b  

^a ETH Zurich ^*  (Germany)

^b ETH ZURICH   (Switzerland)

Author keywords

Gamma function; Psi function; Tur n type inequality

Indexed keywords

EID: 54249088811     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.09.053     Document Type: Article

References (23)

1. In: Abramowitz M., and Stegun I.A. (Eds). Handbook of Mathematical Functions with Formulas, Graphs, and Tables (1965), Dover, New York
2. Alzer H. On some inequalities for the gamma and psi functions. Math. Comp. 66 (1997) 373-389
3. Alzer H. A power mean inequality for the gamma function. Monatsh. Math. 131 (2000) 179-188
4. Alzer H. Mean-value inequalities for the polygamma functions. Aequationes Math. 61 (2001) 151-161
5. Alzer H., and Wells J. Inequalities for the polygamma functions. SIAM J. Math. Anal. 29 (1998) 1459-1466
6. Baricz A. Turán type inequalities for generalized complete elliptic integrals. Math. Z. 256 (2007) 895-911
7. Csordas G., Norfolk T.S., and Varga R.S. The Riemann hypothesis and the Turán inequalities. Trans. Amer. Math. Soc. 296 (1986) 521-541
8. DeTemple D.W., and Robertson J.M. On generalized symmetric means of two variables. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 634-677 (1979) 236-238
9. Dimitrov D.K. Higher order Turán inequalities. Proc. Amer. Math. Soc. 126 (1998) 2033-2037
10. Eliezer C.J., and Daykin D.E. Generalizations and applications of Cauchy-Schwarz inequalities. Quart. J. Math. Oxford (2) 18 (1967) 357-360
11. Engel K. On the average rank of an element in a filter of the partition lattice. J. Combin. Theory Ser. A 64 (1994) 67-78
12. Gautschi W. The incomplete gamma function since Tricomi. Tricomi's Ideas and Contemporary Applied Mathematics. Atti Convegni Lincei vol. 147 (1998), Accad. Naz. Lincei, Rome 203-237
13. Karlin S., and Szegö G. On certain determinants whose elements are orthogonal polynomials. J. Anal. Math. 8 (1960/1961) 1-157
14. Laforgia A., and Natalini P. Inequalities and Turanians for some special functions. Difference Equations, Special Functions and Orthogonal Polynomials, Proc. Int. Conf. Munich, 2005 (2007), World Scientific 422-431
15. Laforgia A., and Natalini P. On some Turán-type inequalities. J. Inequal. Appl. (2006) Article ID 29828, 6 pp
16. Laforgia A., and Natalini P. Turán-type inequalities for some special functions. J. Inequal. Pure Appl. Math. 7 1 (2006) Article 32, 3 pp
17. O'Shea S. A class of power series with no real zeros. Quart. J. Math. Oxford (2) 22 (1971) 143-146
18. Panaitopol L. Erdös-Turán type inequalities. J. Inequal. Pure Appl. Math. 4 1 (2003) Article 23, 5 pp
19. n + 1. Aequationes Math. 20 (1980) 23-32
20. Sándor J. A bibliography on gamma functions: Inequalities and applications. http://math.ubbcluj.ro/~jsandor/letolt/art.pdf
21. Simic S. Turán's inequality for Appell polynomials. J. Inequal. Appl. (2006) Article ID 91420, 7 pp
22. Turán P. On the zeros of the polynomials of Legendre. Časopis Pěst. Mat. Fys. 75 (1950) 113-122
23. Wright E.M. A generalisation of Schur's inequality. Math. Gaz. 40 (1956) 217