The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A242969

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A242969

Decimal expansion of an Ising constant related to the hexagonal lattice.
(history; published version)

#5 by Bruno Berselli at Wed May 28 18:45:40 EDT 2014

STATUS

reviewed

approved

#4 by Joerg Arndt at Wed May 28 14:12:44 EDT 2014

STATUS

proposed

reviewed

Discussion

Wed May 28

18:45

Bruno Berselli: I agree!

#3 by Jean-François Alcover at Wed May 28 05:54:11 EDT 2014

STATUS

editing

proposed

Discussion

Wed May 28

14:12

Joerg Arndt: @other editors: Jean-Francois is doing a very valuable contribution by adding Finch's constants to the OEIS.  I am quite sure Finch himself will be delighted.

#2 by Jean-François Alcover at Wed May 28 05:53:20 EDT 2014

NAME

allocated for Jean-François Alcover

Decimal expansion of an Ising constant related to the hexagonal lattice.

DATA

1, 0, 2, 5, 0, 5, 9, 0, 9, 6, 4, 7, 1, 3, 1, 3, 2, 2, 0, 1, 7, 4, 4, 7, 3, 0, 0, 8, 3, 6, 4, 4, 7, 7, 7, 0, 2, 7, 8, 9, 9, 2, 5, 0, 0, 7, 6, 1, 1, 5, 4, 8, 7, 6, 0, 1, 5, 7, 5, 9, 9, 1, 7, 6, 1, 0, 7, 3, 3, 9, 2, 7, 5, 2, 9, 8, 5, 8, 6, 9, 0, 2, 1, 2, 6, 0, 7, 0, 1, 1, 3, 5, 6, 3, 3, 5, 6, 6, 0, 6

OFFSET

1,3

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising constants, p. 399.

FORMULA

3/4*log(2) + log(3)/2 + H/4, where H is defined in A242967.

EXAMPLE

1.0250590964713132201744730083644777...

MATHEMATICA

H = Sqrt[3]/(6*Pi)*PolyGamma[1, 1/6] - Pi/Sqrt[3] - Log[6]; 3/4*Log[2] + Log[3]/2 + H/4 // RealDigits[#, 10, 100]& // First

CROSSREFS

Cf. A242967, A242968.

KEYWORD

allocated

nonn,cons

AUTHOR

Jean-François Alcover, May 28 2014

STATUS

approved

editing

#1 by Jean-François Alcover at Wed May 28 05:48:23 EDT 2014

NAME

allocated for Jean-François Alcover

KEYWORD

allocated

STATUS

approved