Comptes Rendus
no. 1-2
Mathematical Analysis
New asymptotic expansions related to Somosʼ quadratic recurrence constant
[Nouveaux développements asymptotiques liés à la constante de récurrence quadratique de Somos]

Présenté par : the Editorial Board

Chao-Ping Chen1
1 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City 454003, Henan Province, China
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 9-12.

Nous obtenons de nouveaux développements asymptotiques de la suite de Somos, en termes de la constante de récurrence quadratique de Somos et des nombres de Bell ordonnés.

We derive new asymptotic expansions related to Somosʼ quadratic recurrence constant, in terms of the ordered Bell numbers.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.01.005
Chao-Ping Chen 1

1 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City 454003, Henan Province, China 
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Chao-Ping Chen. New asymptotic expansions related to Somosʼ quadratic recurrence constant. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 9-12. doi : 10.1016/j.crma.2013.01.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.005/

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[2] J. Guillera; J. Sondow Double integrals and infinite products for some classical constants via analytic continuations of Lerchʼs transcendent, Ramanujan J., Volume 16 (2008), pp. 247-270

[3] Kh. Hessami Pilehrood; T. Hessami Pilehrood Arithmetical properties of some series with logarithmic coefficients, Math. Z., Volume 255 (2007), pp. 117-131

[4] Kh. Hessami Pilehrood; T. Hessami Pilehrood Vacca-type series for values of the generalized Euler constant function and its derivative, J. Integer Seq., Volume 13 (2010) (Article 10.7.3)

[5] V. Lampret Approximation of Sondowʼs generalized-Euler-constant function on the interval [−1,1], Ann. Univ. Ferrara, Volume 56 (2010), pp. 65-76

[6] C. Mortici Estimating the Somosʼ quadratic recurrence constant, J. Number Theory, Volume 130 (2010), pp. 2650-2657

[7] G. Nemes On the coefficients of an asymptotic expansion related to Somosʼ quadratic recurrence constant, Appl. Anal. Discrete Math., Volume 5 (2011), pp. 60-66

[8] M. Somos, Several constants related to quadratic recurrences, 1999, unpublished note.

[9] J. Sondow; P. Hadjicostas The generalized-Euler-constant function γ(z) and a generalization of Somosʼs quadratic recurrence constant, J. Math. Anal. Appl., Volume 332 (2007), pp. 292-314

[10] E.W. Weisstein Somosʼs quadratic recurrence constant http://mathworld.wolfram.com/SomossQuadraticRecurrenceConstant.html (MathWorld—A Wolfram Web Resource. Published electronically at)

[11] H.S. Wilf Generating Functionology, A.K. Peters, Ltd., 2006

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