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
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