# zbMATH — the first resource for mathematics

New inequalities for gamma and digamma functions. (English) Zbl 1437.33003
Summary: By using the mean value theorem and logarithmic convexity, we obtain some new inequalities for gamma and digamma functions.
##### MSC:
 33B15 Gamma, beta and polygamma functions
Full Text:
##### References:
 [1] Alzer, H.; Ruscheweyh, S., A subadditive property of the gamma function, Journal of Mathematical Analysis and Applications, 285, 2, 564-577 (2003) · Zbl 1129.33300 [2] Alzer, H., Some gamma function inequalities, Mathematics of Computation, 60, 201, 337-346 (1993) · Zbl 0802.33001 [3] Boyd, A. V., Gurland’s inequality for the gamma function, Scandinavian Actuarial Journal, 1960, 134-135 (1960) · Zbl 0104.37905 [4] Bustoz, J.; Ismail, M. E. H., On gamma function inequalities, Mathematics of Computation, 47, 176, 659-667 (1986) · Zbl 0607.33002 [5] Chen, C. P., Asymptotic expansions of the logarithm of the gamma function in the terms of the polygamma functions, Mathematical Inequalities and Applications, 2, 521-530 (2014) · Zbl 1294.33002 [6] Chen, C.-P., Some properties of functions related to the gamma, psi and tetragamma functions, Computers & Mathematics with Applications, 62, 9, 3389-3395 (2011) · Zbl 1236.33002 [7] Chen, C. P., Unified treatment of several asymptotic formulas for the gamma function, Numerical Algorithms, 64, 2, 311-319 (2013) · Zbl 1280.33003 [8] Erber, T., The gamma function inequalities of Gurland and Gautschi, 1960, 1-2, 27-28 (1960) · Zbl 0104.29204 [9] Keckic, J. D.; Vasic, P. M., Some inequalities for the gamma function, Publications de l’Institut Mathématique, 11, 107-114 (1971) · Zbl 0222.33001 [10] Laforgia, A., Further inequalities for the gamma function, Mathematics of Computation, 42, 166, 597-600 (1984) · Zbl 0536.33003 [11] Lu, D.; Wang, X., A new asymptotic expansion and some inequalities for the gamma function, Journal of Number Theory, 140, 314-323 (2014) · Zbl 1296.33006 [12] Mortici, C., A continued fraction approximation of the gamma function, Journal of Mathematical Analysis and Applications, 402, 2, 405-410 (2013) · Zbl 1333.40001 [13] Mortici, C., Best estimates of the generalized Stirling formula, Applied Mathematics and Computation, 215, 11, 4044-4048 (2010) · Zbl 1186.33003 [14] Mortici, C.; Cristea, V. G.; Lu, D., Completely monotonic functions and inequalities associated to some ratio of gamma function, Applied Mathematics and Computation, 240, 168-174 (2014) · Zbl 1334.33010 [15] Mortici, C., Estimating gamma function by digamma function, Mathematical and Computer Modelling, 52, 5-6, 942-946 (2010) · Zbl 1202.33005 [16] Mortici, C., New approximation formulas for evaluating the ratio of gamma functions, Mathematical and Computer Modelling, 52, 1-2, 425-433 (2010) · Zbl 1201.33003 [17] Mortici, C., New improvements of the Stirling formula, Applied Mathematics and Computation, 217, 2, 699-704 (2010) · Zbl 1202.33004 [18] Mortici, C., Ramanujan formula for the generalized Stirling approximation, Applied Mathematics and Computation, 217, 6, 2579-2585 (2010) · Zbl 1211.40005 [19] Batir, N., Some new inequalities for gamma and polygamma functions, Journal of Inequalities in Pure and Applied Mathematics, 6, 4, article 103 (2005) · Zbl 1089.33001 [20] English, B. J.; Rousseau, G., Bounds for certain harmonic sums, Journal of Mathematical Analysis and Applications, 206, 2, 428-441 (1997) · Zbl 0873.40003 [21] Dence, T. P.; Dence, J. B., A survey of Euler’s constant, American Mathematical Monthly, 82, 225-265 (2009) · Zbl 1227.11128 [22] Artin, E., The Gamma Function (Trans M. Butter) (1964), San Francisco, Calif, USA: Holt, Rinehart and Winston, San Francisco, Calif, USA · Zbl 0144.06802
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.