Abstract
The purpose of this paper is to give some sequences that converge quickly to Ioachimescu’s constant related to Ramanujan formula by multiple-correction method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ioachimescu A.G.: Problem 16. Gaz. Mat. 1(2), 39 (1895)
Sîntămărian A.: Some inequalities regarding a generalization of Ioachimescu’s constant. J. Math. Inequal. 4(3), 413–421 (2010)
Sîntămărian A.: Regarding a generalisation of Ioachimescu’s constant. Math. Gaz. 94(530), 270–283 (2010)
Chen C.P., Li L., Xu Y.Q.: Ioachimescu’s constant. Proc. Jangjeon Math. Soc. 13, 299–304 (2010)
Ramanujan S.: On the sum of the square roots of the first n natural numbers. J. Indian Math. Soc. 7, 173–175 (1915)
Sîntămărian A.: A generalisation of Ioachimescu’s constant. Math. Gaz. 93(528), 456–467 (2009)
Sîntămărian A.: Some sequences that converge to a generalization of Ioachimescu’s constant. Automat. Comput. Appl. Math. 18(1), 177–185 (2009)
Sîntămărian A.: Sequences that converge to a generalization of Ioachimescu’s constant. Sci. Stud. Res., Ser. Math. Inform. 20(2), 89–96 (2010)
Sîntămărian A.: Sequences that converge quickly to a generalized Euler constant. Math. Comput. Modelling 53, 624–630 (2011)
Sîntămărian A.: Some new sequences that converge to a generalized Euler constant. Appl. Math. Lett. 25, 941–945 (2012)
Mortici C., Villariono Mark B.: On the Ramanujan-Lodge harmonic number expansion. Appl. Math. Comput. 251, 423–430 (2015)
Mortici C., Chen C.-P.: On the harmonic number expansion by Ramanujan. J. Inequal. Appl. 2013, 222 (2013)
Mortici C., Berinde V.: New sharp estimates of the generalized Euler–Mascheroni constant. Math. Inequal. Appl. 16(1), 279–288 (2013)
Mortici C., Chen C.-P.: New sequence converging towards the Euler-Mascheroni constant. Comput. Math. Appl. 64(4), 391–398 (2012)
Mortici C.: Fast convergences toward Euler-Mascheroni constant. Comput. Appl. Math. 29(3), 479–491 (2010)
Mortici C.: On some Euler–Mascheroni type sequences. Comput. Math. Appl. 60(7), 2009–2014 (2010)
Mortici C.: Optimizing the rate of convergence in some new classes of sequences convergent to Euler’s constant. Anal. Appl. (Singapore) 8(1), 99–107 (2010)
Cao X.D., Xu H.M., You X.: Multiple-correction and faster approximation. J. Number Theory 149, 327–350 (2015)
Cao X.D.: Multiple-correction and continued fraction approximation. J. Math. Anal. Appl. 424, 1425–1446 (2015)
Cao X.D., You X.: Multiple-correction and continued fraction approximation(II). Appl. Math. Comput. 261, 192–205 (2015)
Xu H.M., You X.: Continued fraction inequalities for the Euler-Mashcheroni constan. J. Inequal. Appl. 2014, 343 (2014)
You X.: Some new quicker convergences to Glaisher–Kinkelin’s and Bendersky–Adamchik’s constants. Appl. Math. Comput. 271, 123–130 (2015)
You X., Chen D.-R.: Improved continued fraction sequence convergent to the Somos’ quadratic recuurence constant. J. Math. Anal. Appl. 436, 513–520 (2016)
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)
Mortici C.: On new sequences converging towards the Euler–Mascheroni constant. Comput. Math. Appl. 59(8), 2610–2614 (2010)
Mortici C.: Product approximations via asymptotic integration. Amer. Math. Month. 117(5), 434–441 (2010)
Ramanujan, S.: The Lost Notebook and Other Unpublished Papers. Narosa, Springer, Berlin (1988)
Karatsuba E.A.: On the asymptotic representation of the Euler gamma function by Ramanujan. J. Comput. Appl. Math. 135(2), 225–240 (2001)
Author information
Authors and Affiliations
Corresponding author
Additional information
We are grateful to the editor and anonymous reviewers for their valuable comments and references that helped improve the original version of this paper. The author is supported by the National Natural Science Foundation of China under Grant 61403034.
Rights and permissions
About this article
Cite this article
You, X. On New Sequences Converging Towards the Ioachimescu’s Constant. Results Math 71, 1491–1498 (2017). https://doi.org/10.1007/s00025-016-0609-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-016-0609-9