Research Article
BibTex RIS Cite

Year 2020, Volume: 3 Issue: 1, 1 - 8, 01.03.2020

Valentin Gabriel Crıstea

https://doi.org/10.33205/cma.608927

Abstract

References

  • M. Abramowitz, I. A. Stegun: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover Publications, 1972.
  • G. D. Anderson, R. W. Barnard, M. K. Vamanamurthy and M. Vuorinen: Inequalities for zero-balanced hypergeometric functions, Trans. Amer. Math. Soc. 347, (1995), 1713-1723.
  • C. P. Chen, L. Lin: Remarks on asymptotic expansions for the gamma function, Appl. Math. Lett. 25 (2012), 2322-2326.
  • V. G. Cristea: Asymptotic series and estimates of a convergence to Euler-Mascheroni constant, J. Sci. Arts, 14 (2) (27)(2014), 143-146.
  • V. G. Cristea, C. Mortici: Latter research on Euler-Mascheroni constant, Contemp. Anal. Appl. Math. 2 (1) (2014),108-115.
  • D. W. DeTemple:A quicker convergences to Euler’s constant, Amer. Math. Monthly, 100 (5) (1993) 468-470.
  • D.W. DeTemple: A geometric look at sequences that convergence to Euler’s constant, College Math. J., 37 (2006) 128-131.
  • R. Graham, D. Knuth and O. Patashnik: Binomial Coefficients. Concrete Mathematics (2nd ed.). AddisonWesley. 153-256, 1994, ISBN 0-201-55802-5.
  • X. Hu, D. Lu and X. Wang: New Quicker Sequences and Inequalities with Continued Fraction Towards Euler’s Constant, Results Math, 73 (1) (2018), 1-10.
  • E. A. Karatsuba: On the computation of the Euler constant Computational methods from rational approximation theory (Wilrijk, 1990), Numer. Algorithms 24 (1-2), (2000), 83-97.
  • C. Mortici: Product approximation via asymptotic integration, Amer. Math. Monthly 117 (5) (2010), 434-441.
  • C. Mortici: Optimizing the rate of convergence in some new classes of sequences convergent to Euler’s constant, Anal. Appl. (Singap.) 8 (1) (2010), 99-107.
  • C. Mortici: Improved convergence towards generalized Euler-Mascheroni constant, Appl. Math. Comput. 215 (9) (2010), 3443-3448.
  • C. Mortici: Fast convergence towards Euler-Mascheroni constant, Comp. Appl. Math. Vol. 29, (3) (2010), 479-491.
  • C. Mortici, A. Vernescu: An improvement of the convergence speed of the sequence $(\gamma _{n})_{n\geq 1}$ converging to Euler’s constant, An. ¸St. Univ. Ovidius Constan¸ta, 13 (1) (2005), 97-100.
  • C. Mortici, A. Vernescu: Some new facts in discrete asymptotic analysis, Math. Balkanika, 21 (3-4) (2007), 301-308.
  • A. Sînt˘am˘arian: A generalization of Euler’s constant, Numer. Algorithms 46 (2) (2007), 141-151.
  • S. R. Tims, J. A. Tyrrell: Approximate evaluation of Euler’s constant, Math. Gaz. 55 (391) (1971) 65-67.
  • R. M. Young: Euler’s constant, Math. Gaz. 75 (472) (1991) 187-190.

A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant

Year 2020, Volume: 3 Issue: 1, 1 - 8, 01.03.2020

Valentin Gabriel Crıstea

https://doi.org/10.33205/cma.608927

Abstract

In this article, we give a new asymptotic series and some estimates for a sequence that converges to Euler-Mascheroni's constant.

Keywords

Euler-Mascheroni's constant asymptotic series inequalities

References

  • M. Abramowitz, I. A. Stegun: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover Publications, 1972.
  • G. D. Anderson, R. W. Barnard, M. K. Vamanamurthy and M. Vuorinen: Inequalities for zero-balanced hypergeometric functions, Trans. Amer. Math. Soc. 347, (1995), 1713-1723.
  • C. P. Chen, L. Lin: Remarks on asymptotic expansions for the gamma function, Appl. Math. Lett. 25 (2012), 2322-2326.
  • V. G. Cristea: Asymptotic series and estimates of a convergence to Euler-Mascheroni constant, J. Sci. Arts, 14 (2) (27)(2014), 143-146.
  • V. G. Cristea, C. Mortici: Latter research on Euler-Mascheroni constant, Contemp. Anal. Appl. Math. 2 (1) (2014),108-115.
  • D. W. DeTemple:A quicker convergences to Euler’s constant, Amer. Math. Monthly, 100 (5) (1993) 468-470.
  • D.W. DeTemple: A geometric look at sequences that convergence to Euler’s constant, College Math. J., 37 (2006) 128-131.
  • R. Graham, D. Knuth and O. Patashnik: Binomial Coefficients. Concrete Mathematics (2nd ed.). AddisonWesley. 153-256, 1994, ISBN 0-201-55802-5.
  • X. Hu, D. Lu and X. Wang: New Quicker Sequences and Inequalities with Continued Fraction Towards Euler’s Constant, Results Math, 73 (1) (2018), 1-10.
  • E. A. Karatsuba: On the computation of the Euler constant Computational methods from rational approximation theory (Wilrijk, 1990), Numer. Algorithms 24 (1-2), (2000), 83-97.
  • C. Mortici: Product approximation via asymptotic integration, Amer. Math. Monthly 117 (5) (2010), 434-441.
  • C. Mortici: Optimizing the rate of convergence in some new classes of sequences convergent to Euler’s constant, Anal. Appl. (Singap.) 8 (1) (2010), 99-107.
  • C. Mortici: Improved convergence towards generalized Euler-Mascheroni constant, Appl. Math. Comput. 215 (9) (2010), 3443-3448.
  • C. Mortici: Fast convergence towards Euler-Mascheroni constant, Comp. Appl. Math. Vol. 29, (3) (2010), 479-491.
  • C. Mortici, A. Vernescu: An improvement of the convergence speed of the sequence $(\gamma _{n})_{n\geq 1}$ converging to Euler’s constant, An. ¸St. Univ. Ovidius Constan¸ta, 13 (1) (2005), 97-100.
  • C. Mortici, A. Vernescu: Some new facts in discrete asymptotic analysis, Math. Balkanika, 21 (3-4) (2007), 301-308.
  • A. Sînt˘am˘arian: A generalization of Euler’s constant, Numer. Algorithms 46 (2) (2007), 141-151.
  • S. R. Tims, J. A. Tyrrell: Approximate evaluation of Euler’s constant, Math. Gaz. 55 (391) (1971) 65-67.
  • R. M. Young: Euler’s constant, Math. Gaz. 75 (472) (1991) 187-190.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Valentin Gabriel Crıstea 0000-0002-9230-425X

Publication Date March 1, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Crıstea, V. G. (2020). A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant. Constructive Mathematical Analysis, 3(1), 1-8. https://doi.org/10.33205/cma.608927
AMA Crıstea VG. A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant. CMA. March 2020;3(1):1-8. doi:10.33205/cma.608927
Chicago Crıstea, Valentin Gabriel. “A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant”. Constructive Mathematical Analysis 3, no. 1 (March 2020): 1-8. https://doi.org/10.33205/cma.608927.
EndNote Crıstea VG (March 1, 2020) A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant. Constructive Mathematical Analysis 3 1 1–8.
IEEE V. G. Crıstea, “A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant”, CMA, vol. 3, no. 1, pp. 1–8, 2020, doi: 10.33205/cma.608927.
ISNAD Crıstea, Valentin Gabriel. “A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant”. Constructive Mathematical Analysis 3/1 (March 2020), 1-8. https://doi.org/10.33205/cma.608927.
JAMA Crıstea VG. A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant. CMA. 2020;3:1–8.
MLA Crıstea, Valentin Gabriel. “A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant”. Constructive Mathematical Analysis, vol. 3, no. 1, 2020, pp. 1-8, doi:10.33205/cma.608927.
Vancouver Crıstea VG. A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant. CMA. 2020;3(1):1-8.
 Download Cover Image