|
|
A261805
|
|
Decimal expansion of M_8, the 8th Madelung constant (negated).
|
|
4
|
|
|
2, 0, 5, 2, 4, 6, 6, 8, 2, 7, 2, 6, 9, 2, 7, 1, 2, 2, 8, 1, 7, 6, 3, 3, 7, 7, 9, 9, 1, 7, 3, 3, 8, 3, 9, 9, 1, 7, 0, 8, 3, 7, 7, 5, 2, 9, 9, 6, 5, 5, 8, 2, 1, 9, 3, 2, 3, 7, 3, 2, 4, 5, 7, 7, 5, 3, 4, 9, 9, 4, 1, 3, 2, 8, 7, 5, 2, 7, 0, 6, 1, 4, 6, 9, 8, 5, 1, 9, 8, 8, 3, 9, 4, 1, 3, 1, 7, 5, 1, 0, 8, 8, 1
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
REFERENCES
|
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.
|
|
LINKS
|
|
|
FORMULA
|
M_8 = (15/(4*Pi^3))*(8*sqrt(2) - 1)*zeta(1/2)*zeta(7/2).
|
|
EXAMPLE
|
-2.052466827269271228176337799173383991708377529965582...
|
|
MATHEMATICA
|
M8 = (15/(4*Pi^3))*(8*Sqrt[2] - 1)*Zeta[1/2]*Zeta[7/2]; RealDigits[M8, 10, 103] // First
|
|
PROG
|
(PARI) th4(x)=1+2*sumalt(n=1, (-1)^n*x^n^2)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|