×

Some sequences converging towards Ioachimescu’s constant related to Ramanujan’s formula. (English) Zbl 1394.11083

Summary: The purpose of this paper is to give some sequences that converge quickly to Ioachimescu’s constant related to Ramanujan’s formula by the multiple-correction method.

MSC:

11Y60 Evaluation of number-theoretic constants
11A55 Continued fractions
41A25 Rate of convergence, degree of approximation
Full Text: DOI

References:

[1] Ioachimescu, A.G.: Problem 16. Gaz. Mat. 1(2), 39 (1895)
[2] Sîntămărian, A.: Some inequalities regarding a generalization of Ioachimescu’s constant. J. Math. Inequal. 4(3), 413-421 (2010) · Zbl 1239.40003 · doi:10.7153/jmi-04-38
[3] Sîntămărian, A.: Regarding a generalisation of Ioachimescu’s constant. Math. Gaz. 94(530), 270-283 (2010) · Zbl 1383.40003 · doi:10.1017/S0025557200006537
[4] Chen, C.P., Li, L., Xu, Y.Q.: Ioachimescu’s constant. Proc. Jangjeon Math. Soc. 13, 299-304 (2010) · Zbl 1245.11128
[5] Ramanujan, S.: On the sum of the square roots of the first n natural numbers. J. Indian Math. Soc. 7, 173-175 (1915)
[6] Sîntămărian, A.: A generalisation of Ioachimescu’s constant. Math. Gaz. 93(528), 456-467 (2009) · Zbl 1169.54022 · doi:10.1017/S0025557200185201
[7] Sîntămărian, A.: Some sequences that converge to a generalization of Ioachimescu’s constant. Autom. Comput. Appl. Math. 18(1), 177-185 (2009)
[8] 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
[9] Sîntămărian, A.: Sequences that converge quickly to a generalized Euler constant. Math. Comput. Model. 53, 624-630 (2011) · Zbl 1217.33004 · doi:10.1016/j.mcm.2010.09.014
[10] Sîntămărian, A.: Some new sequences that converge to a generalized Euler constant. Appl. Math. Lett. 25, 941-945 (2012) · Zbl 1277.40003 · doi:10.1016/j.aml.2011.10.040
[11] Cao, X.D., Xu, H.M., You, X.: Multiple-correction and faster approximation. J. Number Theory. 149, 327-350 (2015) · Zbl 1369.11107 · doi:10.1016/j.jnt.2014.10.016
[12] Cao, X.D.: Multiple-correction and continued fraction approximation. J. Math. Anal. Appl. 424, 1425-1446 (2015) · Zbl 1306.11099 · doi:10.1016/j.jmaa.2014.12.014
[13] Cao, X.D., You, X.: Multiple-correction and continued fraction approximation(II). Appl. Math. Comput. 261, 192-205 (2015) · Zbl 1397.11165
[14] Xu, H.M., You, X.: Continued fraction inequalities for the Euler-Mascheroni constant. J. Inequal. Appl. 2014, 343 (2014) · Zbl 1332.11111 · doi:10.1186/1029-242X-2014-343
[15] You, X.: Some new quicker convergences to Glaisher-Kinkelin’s and Bendersky-Adamchik’s constants. Appl. Math. Comput. 271, 123-130 (2015) · Zbl 1410.11139
[16] You, X., Chen, D.-R.: Improved continued fraction sequence convergent to the Somos’ quadratic recurrence constant. J. Math. Anal. Appl. 436, 513-520 (2016) · Zbl 1378.11109 · doi:10.1016/j.jmaa.2015.12.013
[17] You, X., Huang, S.Y., Chen, D.-R.: Some new continued fraction sequence convergent to the Somos’ quadratic recurrence constant. J. Inequal. Appl. 2016, 91 (2016) · Zbl 1353.40001 · doi:10.1186/s13660-016-1035-y
[18] Mortici, C.: On new sequences converging towards the Euler-Mascheroni constant. Comput. Math. Appl. 59(8), 2610-2614 (2010) · Zbl 1193.33003 · doi:10.1016/j.camwa.2010.01.029
[19] Mortici, C.: Product approximations via asymptotic integration. Am. Math. Month. 117(5), 434-441 (2010) · Zbl 1214.40002 · doi:10.4169/000298910x485950
[20] Ramanujan, S.: The Lost Notebook and Other Unpublished Papers. Springer, New Delhi (1988) · Zbl 0639.01023
[21] Karatsuba, E.A.: On the asymptotic representation of the Euler gamma function by Ramanujan. J. Comput. Appl. Math. 135(2), 225-240 (2001) · Zbl 0988.33001 · doi:10.1016/S0377-0427(00)00586-0
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.