Investigations about the Euler–Mascheroni constant and harmonic numbers

References

[1] Boas R. P., Growth of partial sums of divergent series, Math. Comp. 31 (1977), 257–264. 10.1090/S0025-5718-1977-0440862-0Search in Google Scholar

[2] Boas R. P. and Wrench I. W., Partial sums of the harmonic series, Amer. Math. Monthly 78 (1971), 864–870. 10.1080/00029890.1971.11992881Search in Google Scholar

[3] Carlson B. C., Some inequalities for hypergeometric functions, Proc. Amer. Math. Soc. 17 (1966), 32–39. 10.1090/S0002-9939-1966-0188497-6Search in Google Scholar

[4] Chen C.-P., Inequalities and monotonicity properties for some special functions, J. Math. Inequal. 3 (2009), 79–91. 10.7153/jmi-03-07Search in Google Scholar

[5] Chen C.-P. and Mortici C., New sequence converging towards the Euler–Mascheroni constant, Comp. Math. Appl. 64 (2012), 391–398. 10.1016/j.camwa.2011.03.099Search in Google Scholar

[6] Comtet L., Problem 5346, Amer. Math. Monthly 74 (1967), 209. 10.2307/2315638Search in Google Scholar

[7] DeTemple D. W., A quicker convergence to Euler’s constant, Amer. Math. Monthly 100 (1993), 468–470. 10.1080/00029890.1993.11990433Search in Google Scholar

[8] DeTemple D. W. and Wang S. H., Half integer approximations for the partial sums of the harmonic series, J. Math. Anal. Appl. 160 (1991), 149–156. 10.1016/0022-247X(91)90296-CSearch in Google Scholar

[9] Erdős P., Problem 672A, Elem. Math. 27 (1972), 68. Search in Google Scholar

[10] Guo B.-N. and Qi F., Sharp inequalities for the psi function and harmonic numbers, Analysis 34 (2014), 201–208. 10.1515/anly-2014-0001Search in Google Scholar

[11] Hessami Pilehrood T., Elem. Math. 70 (2015), 177. Search in Google Scholar

[12] Mortici C. and Rassias M. T., On the growth rate of divergent series, J. Number Th. 147 (2015), 499–507. 10.1016/j.jnt.2014.07.025Search in Google Scholar

[13] Mortici C. and Villarino M. B., On the Ramanujan-Lodge harmonic number expansion, Appl. Math. and Comp. 251 (2015), 423–430. 10.1016/j.amc.2014.11.088Search in Google Scholar

[14] Newton R. H. C., Problem 5989, Amer. Math. Monthly 81 (1974), 910. 10.1080/00029890.1974.11993693Search in Google Scholar

[15] Niu D.-W., Dong L.-S. and Cao J., Three new sequences converging to the Euler–Mascheroni constant, Analysis 33 (2013), 389–399. 10.1524/anly.2013.1174Search in Google Scholar

[16] Rippon P. J., Convergence with pictures, Amer. Math. Monthly 93 (1986), 476–478. 10.1080/00029890.1986.11971862Search in Google Scholar

[17] Young R. M., Euler’s constant, Math. Gaz. 75 (1991), 187–190. 10.2307/3620251Search in Google Scholar

[18] Zemyan S. M., On two conjectures concerning the partial sums of the harmonic series, Proc. Amer. Math. Soc. 95 (1985), 83–86. 10.1090/S0002-9939-1985-0796451-8Search in Google Scholar