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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.31 no.1 Antofagasta mar. 2012

http://dx.doi.org/10.4067/S0716-09172012000100004 

Proyecciones Journal of Mathematics Vol. 31, No 1, pp. 29-38, March 2012. Universidad Católica del Norte Antofagasta - Chile

 

Improving some sequences convergent to Euler-Mascheroni constant

 

Necdet Batir

Nevsehir University, Nevsehir, Turkey

Chao-Ping Chen

Henan Polytechnic University, China


ABSTRACT

We obtain the following very fast sequences convergent to Euler-Mascheroni constant:

= H ( 1 J_ _J_ 23 17 10099 \

n = n־ ogVn + 2 + 24n 48 ־n2 + 5760n3 + 3840n4 2903040 ־n5 )

and

= H ( 1 1___37 10313 \

öç = Hn lo^n + 2 + 24(n + é) 5760(n + 2)3 + 2903040(n + 2 f) '

where Hn are the harmonic numbers defined by Hn = 1+2 +1+... + n·

subjclass [2000] : Primary 11Y60; Secondary 40A05.

Keywords : Euler-Mascheroni constant, harmonic numbers, in-equalities, asymptotic expansion.


 

 

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Necdet Batir

Department of Mathematics, Faculty of Arts and Sciences, Nevsehir University, Nevsehir, Turkey

e-mail : nbatir@hotmail.com and

Chao-Ping Chen

School of Mathematics and Informatics, Henan Polytechnic University,

Jiaozuo City 454003,

Henan Province,

People's Republic of China

e-mail : chenchaoping@sohu.com

Received : November 2011. Accepted : December 2011