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A355953
Decimal expansion of (gamma + log(8)/2)/Pi.
4
5, 1, 4, 6, 8, 6, 8, 5, 2, 8, 2, 7, 2, 8, 5, 3, 7, 0, 8, 5, 3, 9, 6, 9, 1, 1, 6, 3, 2, 0, 7, 5, 2, 7, 1, 9, 3, 0, 1, 2, 9, 3, 1, 8, 4, 2, 1, 5, 7, 6, 5, 6, 3, 0, 4, 5, 6, 0, 6, 9, 2, 6, 7, 3, 0, 9, 8, 0, 8, 2, 8, 9, 2, 6, 9, 2, 6, 6, 1, 6, 5, 0, 0, 5, 4
OFFSET
0,1
COMMENTS
This constant is the additive part A in the asymptotic behavior of the resistance R between two nodes in an infinite square lattice of one-ohm resistors separated by the distance vector (i,j): R(i,j) = log(sqrt(i^2+j^2))/Pi + A. From an engineering point of view, this constant summand can be regarded as a kind of near-field contribution, which contains the well-known resistance of 1/2 ohms between 2 neighboring nodes as the main part.
See, e.g., Cserti (1999) formula (33) on page 5 and Appendix B, pages 15 and 16, for a derivation of the parts of the constant.
LINKS
József Cserti, Application of the lattice Green's function for calculating the resistance of an infinite network of resistors, American Journal of Physics, Vol. 68, No. 10 (2000), pp. 896-906; arXiv preprint, arXiv:cond-mat/9909120 [cond-mat.mes-hall], 1999-2000.
EXAMPLE
0.5146868528272853708539691163207527193...
MATHEMATICA
RealDigits[(EulerGamma + Log[8]/2)/Pi, 10, 120][[1]] (* Amiram Eldar, Jun 18 2023 *)
PROG
(PARI) (Euler + log(8)/2)/Pi
CROSSREFS
Cf. A001620, A016631, A355955, A355954 (similar for triangular lattice).
Cf. A355565, A355566, A355567 (exact solutions for small distances).
Sequence in context: A216851 A179290 A342014 * A167864 A232809 A011301
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Jul 26 2022
STATUS
approved