|
Search: id:A074962
|
|
|
| A074962 |
|
Decimal expansion of Glaisher-Kinkelin constant A. |
|
+0
5
|
|
| 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, 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, 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
(list; cons; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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.
|
|
REFERENCES
|
K. Knopp, "Theory and applications of infinite series", Dover, p. 555
S. R. Finch, Mathematical constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 135
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant
|
|
FORMULA
|
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))
|
|
PROGRAM
|
(PARI) x=10^(-100); exp(1/12-(zeta(-1+x)-zeta(-1))/x)
|
|
CROSSREFS
|
Sequence in context: A065813 A076344 A090975 this_sequence A064863 A021358 A141449
Adjacent sequences: A074959 A074960 A074961 this_sequence A074963 A074964 A074965
|
|
KEYWORD
|
cons,nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 05 2002
|
|
EXTENSIONS
|
More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Feb 03 2003
|
|
|
Search completed in 0.002 seconds
|
