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Approximation properties related to the Bell polynomials

Year 2021, , 253 - 259, 01.06.2021
https://doi.org/10.33205/cma.861342

Abstract

The authors provide a complete asymptotic expansion for a class of functions in terms of the complete
Bell polynomials. In particular, they obtain known asymptotic expansions of some Keller type sequences.

References

  • E. Maor: e: the story of a number, Princeton University Press, Princeton, NJ (2009).
  • J. Sandor: On certain limits related to the number e, Libertas Math., 20 (2000) 155–159, dedicated to Emeritus Professor Corneliu Constantinescu on the occasion of his 70th birthday.
  • S. R. Finch: Mathematical constants, Vol. 94 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (2003).
  • H. J. Brothers, J. A. Knox: New closed-form approximations to the logarithmic constant e, Math. Intelligencer, 20 (4) (1998), 25–29.
  • H. Alzer, C. Berg: Some classes of completely monotonic functions, Ann. Acad. Sci. Fenn. Math., 27 (2) (2002), 445–460.
  • C. Mortici, Y. Hu: On an infinite series for (1 + 1=x)x (Jun 2014). http://arxiv.org/abs/1406.7814v1
  • Y. Hu, C. Mortici: On the Keller limit and generalization, J. Inequal. Appl., 2016 (2016), 97.
  • J. Riordan: An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London (1958).
  • L. Comtet: Advanced combinatorics, enlarged Edition, D. Reidel Publishing Co., Dordrecht (1974).
  • J. A. Knox, H. J. Brothers: Novel series-based approximations to e, College Math. J., 30 (4) (1999), 269–275.
  • C. Mortici, X.-J. Jang: Estimates of (1+x)1=x involved in Carleman’s inequality and Keller’s limit, Filomat, 29 (7) (2015), 1535–1539.
  • X. Yang: Approximations for constant e and their applications, J. Math. Anal. Appl., 262 (2) (2001), 651–659.
Year 2021, , 253 - 259, 01.06.2021
https://doi.org/10.33205/cma.861342

Abstract

References

  • E. Maor: e: the story of a number, Princeton University Press, Princeton, NJ (2009).
  • J. Sandor: On certain limits related to the number e, Libertas Math., 20 (2000) 155–159, dedicated to Emeritus Professor Corneliu Constantinescu on the occasion of his 70th birthday.
  • S. R. Finch: Mathematical constants, Vol. 94 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (2003).
  • H. J. Brothers, J. A. Knox: New closed-form approximations to the logarithmic constant e, Math. Intelligencer, 20 (4) (1998), 25–29.
  • H. Alzer, C. Berg: Some classes of completely monotonic functions, Ann. Acad. Sci. Fenn. Math., 27 (2) (2002), 445–460.
  • C. Mortici, Y. Hu: On an infinite series for (1 + 1=x)x (Jun 2014). http://arxiv.org/abs/1406.7814v1
  • Y. Hu, C. Mortici: On the Keller limit and generalization, J. Inequal. Appl., 2016 (2016), 97.
  • J. Riordan: An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London (1958).
  • L. Comtet: Advanced combinatorics, enlarged Edition, D. Reidel Publishing Co., Dordrecht (1974).
  • J. A. Knox, H. J. Brothers: Novel series-based approximations to e, College Math. J., 30 (4) (1999), 269–275.
  • C. Mortici, X.-J. Jang: Estimates of (1+x)1=x involved in Carleman’s inequality and Keller’s limit, Filomat, 29 (7) (2015), 1535–1539.
  • X. Yang: Approximations for constant e and their applications, J. Math. Anal. Appl., 262 (2) (2001), 651–659.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ioan Gavrea This is me

Mircea Ivan 0000-0001-6047-2470

Publication Date June 1, 2021
Published in Issue Year 2021

Cite

APA Gavrea, I., & Ivan, M. (2021). Approximation properties related to the Bell polynomials. Constructive Mathematical Analysis, 4(2), 253-259. https://doi.org/10.33205/cma.861342
AMA Gavrea I, Ivan M. Approximation properties related to the Bell polynomials. CMA. June 2021;4(2):253-259. doi:10.33205/cma.861342
Chicago Gavrea, Ioan, and Mircea Ivan. “Approximation Properties Related to the Bell Polynomials”. Constructive Mathematical Analysis 4, no. 2 (June 2021): 253-59. https://doi.org/10.33205/cma.861342.
EndNote Gavrea I, Ivan M (June 1, 2021) Approximation properties related to the Bell polynomials. Constructive Mathematical Analysis 4 2 253–259.
IEEE I. Gavrea and M. Ivan, “Approximation properties related to the Bell polynomials”, CMA, vol. 4, no. 2, pp. 253–259, 2021, doi: 10.33205/cma.861342.
ISNAD Gavrea, Ioan - Ivan, Mircea. “Approximation Properties Related to the Bell Polynomials”. Constructive Mathematical Analysis 4/2 (June 2021), 253-259. https://doi.org/10.33205/cma.861342.
JAMA Gavrea I, Ivan M. Approximation properties related to the Bell polynomials. CMA. 2021;4:253–259.
MLA Gavrea, Ioan and Mircea Ivan. “Approximation Properties Related to the Bell Polynomials”. Constructive Mathematical Analysis, vol. 4, no. 2, 2021, pp. 253-9, doi:10.33205/cma.861342.
Vancouver Gavrea I, Ivan M. Approximation properties related to the Bell polynomials. CMA. 2021;4(2):253-9.