Search: id:A074962
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%I A074962
%S A074962 1,2,8,2,4,2,7,1,2,9,1,0,0,6,2,2,6,3,6,8,7,5,3,4,2,5,6,8,8,6,9,7,9,1,7,
%T A074962 2,7,7,6,7,6,8,8,9,2,7,3,2,5,0,0,1,1,9,2,0,6,3,7,4,0,0,2,1,7,4,0,4,0,6,
%U A074962 3,0,8,8,5,8,8,2,6,4,6,1,1,2,9,7,3,6,4,9,1,9,5,8,2,0,2,3,7,4,4,1,0,2,4
%N A074962 Decimal expansion of Glaisher-Kinkelin constant A.
%C A074962 Arise in various asymptotic expressions such as A002109(n)=1^1*2^2*3^3*...*n^n 
               which is asymptotic to A*n^(n^2/2+n/2+1/12)*exp(-n^2/4). See A002109 
               for more references and links.
%D A074962 K. Knopp, "Theory and applications of infinite series", Dover, p. 555
%D A074962 S. R. Finch, Mathematical constants, Encyclopedia of Mathematics and 
               its Applications, vol. 94, Cambridge University Press, p. 135
%H A074962 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>
%F A074962 A=1.2824271291... A = 2^(1/36)*Pi^(1/6)*exp(1/3*(-Gamma/4+s(2)/3-s(3)/
               4+...)) where s(k) denotes sum(n>=0, 1/(2n+1)^k) . Closed expressions 
               for A are exp(-zeta'(2)/2/Pi^2 + log(2*Pi)/12 + Gamma/12) or exp(1/
               12-zeta'(-1))
%o A074962 (PARI) x=10^(-100); exp(1/12-(zeta(-1+x)-zeta(-1))/x)
%Y A074962 Sequence in context: A065813 A076344 A090975 this_sequence A064863 A021358 
               A141449
%Y A074962 Adjacent sequences: A074959 A074960 A074961 this_sequence A074963 A074964 
               A074965
%K A074962 cons,nonn
%O A074962 1,2
%A A074962 Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 05 2002
%E A074962 More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Feb 03 
               2003

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