|
Search: id:A068982
|
|
|
| A068982 |
|
Limit of the product of a modified Zeta function. |
|
+0
1
|
|
| 4, 3, 5, 7, 5, 7, 0, 7, 3, 1, 2, 2, 1, 8, 7, 0, 4, 2, 9, 2
(list; cons; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
The "modified Zeta function" Zetam(n) = sum(mu(k)/k^n) may be helpful when searching for a closed form for Apery's constant. I used the first 100000 terms to get the sum and the first 106 terms to get the product. It took me 3 days of Maple 7 calculations to get these first 20 digits using a precision of 35 digits.
|
|
FORMULA
|
Product(Sum(mu(k)/k^n)), k=1..infinity, n=2..infinity
|
|
EXAMPLE
|
0.43575707312218704292...
|
|
MAPLE
|
with(numtheory); evalf(Product(Sum('mobius(k)/k^n', 'k'=1..infinity), n=2..infinity), 40); Note: For practical reasons you should change "infinity" to some finite value.
|
|
CROSSREFS
|
Cf. A021002, A002117.
Adjacent sequences: A068979 A068980 A068981 this_sequence A068983 A068984 A068985
Sequence in context: A023829 A000211 A059902 this_sequence A035427 A010475 A033546
|
|
KEYWORD
|
cons,more,nonn
|
|
AUTHOR
|
Andre Neumann Kauffman (andrekff(AT)hotmail.com), Apr 01 2002
|
|
|
Search completed in 0.002 seconds
|
