Some new sequences that converge to a generalized Euler constant. (English) Zbl 1277.40003
There are constructed some sequences converging to a generalized Euler constant. Speed of convergence is estimated using Cesàro-Stolz lemma.
Reviewer: Cristinel Mortici (Târgovişte)
MSC:
| 40A05 | Convergence and divergence of series and sequences |
| 33B15 | Gamma, beta and polygamma functions |
| 11Y60 | Evaluation of number-theoretic constants |
| 11B68 | Bernoulli and Euler numbers and polynomials |
Keywords:
sequence; convergence; generalized Euler constant; Ioachimescu’s constant; Bernoulli number; Euler-Maclaurin summation formulaReferences:
| [1] | Finch, S. R., Mathematical Constants (2003), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1054.00001 |
| [2] | Sîntămărian, A., Some inequalities regarding a generalization of Ioachimescu’s constant, J. Math. Inequal., 4, 3, 413-421 (2010) · Zbl 1239.40003 |
| [3] | Ioachimescu, A. G., Problem 16, Gaz. Mat., 1, 2, 39 (1895) |
| [4] | Ramanujan, S., On the sum of the square of the first \(n\) natural numbers, J. Indian Math. Soc., 7, 173-175 (1915) |
| [5] | Ramanujan, S., (Hardy, G. H.; Seshu Aiyar, P. V.; Wilson, B. M.; Berndt, B. C., Collected Papers of Srinivasa Ramanujan (2000), AMS Chelsea Publishing: AMS Chelsea Publishing Providence, Rhode Island) · Zbl 1110.11001 |
| [6] | Sîntămărian, A., Probleme Selectate cu Şiruri de Numere Reale (Selective Problems with Sequences of Real Numbers) (2008), Editura U. T. Press: Editura U. T. Press Cluj-Napoca |
| [7] | Sîntămărian, A., Regarding a generalisation of Ioachimescu’s constant, Math. Gaz., 94, 530, 270-283 (2010) · Zbl 1383.40003 |
| [8] | Havil, J., Gamma: Exploring Euler’s Constant (2003), Princeton University Press: Princeton University Press Princeton and Oxford · Zbl 1023.11001 |
| [9] | Knopp, K., Theory and Application of Infinite Series (1951), Blackie & Son Limited: Blackie & Son Limited London, Glasgow · JFM 54.0222.09 |
| [10] | Sîntămărian, A., A generalisation of Ioachimescu’s constant, Math. Gaz., 93, 528, 456-467 (2009) |
| [11] | Sîntămărian, A., Some sequences that converge to a generalization of Ioachimescu’s constant, Automat. Comput. Appl. Math., 18, 1, 177-185 (2009) |
| [12] | Sîntămărian, A., Sequences that converge to a generalization of Ioachimescu’s constant, Sci. Stud. Res., Ser. Math. Inform., 20, 2, 89-96 (2010) · Zbl 1265.40014 |
| [13] | Sîntămărian, A., Some new sequences that converge to a generalization of Ioachimescu’s constant, Automat. Comput. Appl. Math., 19, 1, 179-191 (2010) |
| [14] | Sîntămărian, A., Sequences that converge quickly to a generalized Euler constant, Math. Comput. Modelling, 53, 5-6, 624-630 (2011) · Zbl 1217.33004 |
| [15] | Hirschhorn, M., On ‘A generalisation of Ioachimescu’s constant’ (feedback), Math. Gaz., 94, 530, 338-341 (2010) |
| [16] | Sondow, J.; Hadjicostas, P., The generalized-Euler-constant function \(\gamma(z)\) and a generalization of Somos’s quadratic recurrence constant, J. Math. Anal. Appl., 332, 1, 292-314 (2007) · Zbl 1113.11017 |
| [17] | Lampret, V., An accurate approximation of zeta-generalized-Euler-constant functions, Cent. Eur. J. Math., 8, 3, 488-499 (2010) · Zbl 1204.33027 |
| [18] | A. Sîntămărian, Some new sequences that converge to a generalization of Euler’s constant, Creat. Math. Inform. (in press).; A. Sîntămărian, Some new sequences that converge to a generalization of Euler’s constant, Creat. Math. Inform. (in press). · Zbl 1274.11183 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
