Alzer, Horst Gamma function inequalities. (English) Zbl 1167.33001 Numer. Algorithms 49, No. 1-4, 53-84 (2008). Some new inequalities for Euler’s gamma function are derived and proved. Reviewer: James Adedayo Oguntuase (Abeokuta) Cited in 5 Documents MSC: 33B15 Gamma, beta and polygamma functions 26D10 Inequalities involving derivatives and differential and integral operators Keywords:Gamma function; inequalities; monotonicity; convexity; mean values PDF BibTeX XML Cite \textit{H. Alzer}, Numer. Algorithms 49, No. 1--4, 53--84 (2008; Zbl 1167.33001) Full Text: DOI Digital Library of Mathematical Functions: §5.6(i) Real Variables ‣ §5.6 Inequalities ‣ Properties ‣ Chapter 5 Gamma Function Kershaw’s Inequality ‣ §5.6(i) Real Variables ‣ §5.6 Inequalities ‣ Properties ‣ Chapter 5 Gamma Function References: [1] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1965), New York: Dover, New York · Zbl 0515.33001 [2] Alsina, C.; Tomás, M. S., A geometrical proof of a new inequality for the gamma function, J. Inequal. Pure Appl. Math., 6, 2, 48 (2005) · Zbl 1082.33001 [3] Alzer, H., Inequalities for the gamma function, Proc. Am, 128, 141-147 (1999) · Zbl 0966.33001 [4] Alzer, H., A power mean inequality for the gamma function, Monatsh. Math., 131, 179-188 (2000) · Zbl 0964.33002 [5] Alzer, H., Mean-value inequalities for the polygamma functions, Aequ. Math., 61, 151-161 (2001) · Zbl 0968.33003 [6] Alzer, H., On a gamma function inequality of Gautschi, Proc. Edinb. Math. Soc., 45, 589-600 (2002) · Zbl 1013.33001 [7] Alzer, H., Inequalities involving Γ (x) and Γ (1/x), J. Comput. Appl. Math., 192, 460-480 (2006) · Zbl 1091.33001 [8] Alzer, H.; Berg, C., Some classes of completely monotonic functions, II, Ramanujan J., 11, 225-248 (2006) · Zbl 1110.26015 [9] Alzer, H.; Ruscheweyh, S., A subadditive property of the gamma function, J. Math. Anal. Appl., 285, 564-577 (2003) · Zbl 1129.33300 [10] Daróczy, Z., On the general solution of the functional equation f(x + y − xy) + f(xy) = f(x) + f(y), Aequ. Math., 6, 130-132 (1971) · Zbl 0222.39003 [11] Davidson, T. M.K., The complete solution of Hosszú’s functional equation over a field, Aequ. Math., 11, 273-276 (1974) · Zbl 0289.39004 [12] Davis, P. J., Leonhard Euler’s integral: a historical profile of the gamma function, Amer. Math. Mon., 66, 849-869 (1959) · Zbl 0091.00506 [13] Gautschi, W., A harmonic mean inequality for the gamma function, SIAM J. Math. Anal., 5, 278-281 (1974) · Zbl 0239.33002 [14] Gautschi, W., Some mean value inequalities for the gamma function, SIAM J. Math. Anal., 5, 282-292 (1974) · Zbl 0239.33003 [15] Gautschi, W., The incomplete gamma function since Tricomi, Tricomi’s Ideas and Contemporary Applied Mathematics, Atti Convegni Lincei, vol. 147, 203-237 (1998), Rome: Accad. Naz. Lincei, Rome · Zbl 0965.33001 [16] Giordano, C.; Laforgia, A., Inequalities and monotonicity properties for the gamma function, J. Comput. Appl. Math., 133, 387-396 (2001) · Zbl 0985.33003 [17] Kershaw, D.; Laforgia, A., Monotonicity results for the gamma function, Atti Accad. Scienze Torino, 119, 127-133 (1985) · Zbl 0805.33001 [18] Kim, T.; Adiga, C., On the q-analogue of gamma functions and related inequalities, J. Inequal. Pure Appl. Math., 6, 4, 118 (2005) · Zbl 1080.33014 [19] Laforgia, A.; Sismondi, S., A geometric mean inequality for the gamma function, Boll. Un. Ital. A, 3, 7, 339-342 (1989) · Zbl 0686.33001 [20] Lucht, L. G., Mittelwertungleichungen für Lösungen gewisser Differenzengleichungen, Aequ. Math., 39, 204-209 (1990) · Zbl 0705.39002 [21] Maksa, G.; Páles, Z., On Hosszú’s functional inequality, Publ. Math. Debrecen, 36, 187-189 (1989) · Zbl 0697.39014 [22] McD. Mercer, A.: Some new inequalities for the gamma, beta and zeta functions. J. Inequal. Pure Appl. Math. 7(1), Art. 29 (2006) · Zbl 1182.33005 [23] Mitrinović, D. S., Analytic Inequalities (1970), New York: Springer, New York · Zbl 0199.38101 [24] Neuman, E., Inequalities involving a logarithmically convex function and their applications to special functions, J. Inequal. Pure Appl. Math., 7, 1, 16 (2006) · Zbl 1132.26337 [25] Sándor, J., A note on certain inequalities for the gamma function, J. Inequal. Pure Appl. Math., 6, 3, 61 (2005) · Zbl 1088.33003 [26] Webster, R. J., cos(sinx) ≥ |cosx| ≥ |sin(cosx)|, Math. Gaz., 68, 37 (1984) [27] Wright, E. M., A generalisation of Schur’s inequality, Math. Gaz., 40, 217 (1956) · Zbl 0074.04002 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.