Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A088537
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A088537 Decimal expansion of Madelung's constant M2. +0
2
1, 6, 1, 5, 5, 4, 2, 6, 2, 6, 7, 1, 2, 8, 2, 4, 7, 2, 3, 8, 6, 7, 9, 2, 3, 3, 3, 2, 7, 5, 8, 6, 1, 8, 0, 9, 0, 1, 9, 6, 4, 2, 2, 9, 2, 3, 6, 1, 3, 7, 7, 7, 1, 4, 5, 6, 9, 3, 7, 3, 5, 3, 5, 9, 6, 1, 2, 6, 5, 1, 2, 3, 1, 6, 1, 5, 3, 3, 3, 6, 2, 9, 0, 4, 1, 6, 5, 8, 9, 5, 5, 1, 7, 1, 8, 7, 2, 1, 4, 5, 5, 7, 4, 9, 0 (list; cons; graph; listen)
OFFSET

1,2

REFERENCES

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 76-81

I. J. Zucker, Exact results for some lattice sums in 2, 4, 6 and 8 dimensions, J. Phys. A: Math., Gen. vol. 7 (1974) no. 13, p 1568-1575.

FORMULA

M2=sum{ -oo < i < oo, -oo < j < oo, (i,j) != (0,0)} (-1)^(i+j)/sqrt(i^2+j^2)).

M2=4*(sqrt(2)-1)*zeta(1/2)*beta(1/2) (beta=Dirichlet beta function).

EXAMPLE

M2=-1.6155426267....

MAPLE

M2:=evalf(4*(sqrt(2)-1)*Zeta(1/2)*sum('(-1)^n/sqrt(2*n+1)', 'n'=0..infinity), 120); [From Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 10 2009]

PROGRAM

(PARI) DirBet=sumalt(n=0, (-1)^n/sqrt(2*n+1)); print(4.0*(sqrt(2)-1)*zeta(0.5)*DirBet) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 20 2007

CROSSREFS

Sequence in context: A010137 A011096 A021623 this_sequence A019847 A021946 A011439

Adjacent sequences: A088534 A088535 A088536 this_sequence A088538 A088539 A088540

KEYWORD

nonn,cons

AUTHOR

Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 16 2003

EXTENSIONS

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 20 2007

Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 10 2009

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 29 12:46 EST 2009. Contains 167659 sequences.


AT&T Labs Research