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On one asymptotic formula for the Euler constant

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Abstract

We derive a new asymptotic representation for the Euler constant γ.

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References

  1. Euler, L., Institutiones Calculi Differentialis cum Eius Vsu in Analysi Finitorum ac Doctrina Serierum, Petropolitanae: Acad. Imper. Sci., 1755.

    Google Scholar 

  2. Berndt, B.C., Ramanujan’s Notebooks, Part 1, New York: Springer, 1985.

    Google Scholar 

  3. Brent, R.P. and McMillan, E.M., Some New Algorithms for High-Precision Computation of Euler’s Constant, Math. Comput., 1980, vol. 34, no. 149, pp. 305–312.

    MathSciNet  MATH  Google Scholar 

  4. Karatsuba, E.A., Fast Evaluation of Transcendental Functions Probl. Peredachi Inf., 1991, vol. 27, no. 4, pp. 87–110 [Probl. Inf. Trans. (Engl. Transl.), 1997, vol. 33, no. 3, pp. 339–360].

    MathSciNet  Google Scholar 

  5. Karatsuba, E.A., On the Computation of the Euler Constant γ, J. Numer. Algorithms, 2000, vol. 24, no. 1–2, pp. 83–97.

    Article  MathSciNet  MATH  Google Scholar 

  6. Aptekarev, A.I. and Tulyakov, D.N., Four-Term Recurrence Relations for γ-Forms, Sovr. Probl. Matem., 2007, vol. 9, pp. 37–43 [Proc. Steklov Inst. Math. (Engl. Transl.), 2011, vol. 272, no. 2 suppl., pp. 157–161].

    Article  Google Scholar 

  7. Aptekarev, A.I. and Lysov, V.G., Asymptotic γ-Forms Generated by Multiple Orthogonal Polynomials, Sovr. Probl. Matem., 2007, vol. 9, pp. 55–62 [Proc. Steklov Inst. Math. (Engl. Transl.), 2011, vol. 272, no. 2 suppl., pp. 168–173].

    Article  Google Scholar 

  8. Karatsuba, E.A., On the Asymptotic Representation of the Euler Gamma Function by Ramanujan, J. Comput. Appl. Math., 2001, vol. 135, no. 2, pp. 225–240.

    Article  MathSciNet  MATH  Google Scholar 

  9. Voronin, S.M. and Karatsuba, A.A., Dzeta-funktsiya Rimana (Riemann Zeta Function), Moscow: Fizmatlit, 1994.

    Google Scholar 

  10. Temme, N.M., Special Functions: An Introduction to the Classical Functions of Mathematical Physics, New York: Wiley, 1996.

    Book  MATH  Google Scholar 

  11. Fikhtengol’ts, G.M., Kurs differentsial’nogo i integral’nogo ischisleniya (A Course in Differential and Integral Calculus), Moscow: Fizmatgiz, 1959, vol. 2.

    Google Scholar 

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Authors and Affiliations

  1. Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, Russia

    E. A. Karatsuba

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  1. E. A. Karatsuba
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Correspondence to E. A. Karatsuba.

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Original Russian Text © E.A. Karatsuba, 2012, published in Problemy Peredachi Informatsii, 2012, Vol. 48, No. 4, pp. 50–55.

Supported in part by the Russian Foundation for Basic Research, project no. 11-07-13160.

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Karatsuba, E.A. On one asymptotic formula for the Euler constant. Probl Inf Transm 48, 342–346 (2012). https://doi.org/10.1134/S0032946012040047

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  • DOI: https://doi.org/10.1134/S0032946012040047

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