A355953 Decimal expansion of (gamma + log(8)/2)/Pi.

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

Author

Hugo Pfoertner, Jul 26 2022

Keywords

• nonn
• cons

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.

Examples

			0.5146868528272853708539691163207527193...
		

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.

Crossrefs

Cf. A001620, A016631, A355955, A355954 (similar for triangular lattice).

Cf. A355565, A355566, A355567 (exact solutions for small distances).

Programs

Mathematica

RealDigits[(EulerGamma + Log[8]/2)/Pi, 10, 120][[1]] (* Amiram Eldar, Jun 18 2023 *)

PARI

(Euler + log(8)/2)/Pi