A259679 Lampard's constant, decimal expansion of log(2)/(4*Pi^2).

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

Offset: 0

Author

Johannes W. Meijer, Jul 03 2015

Keywords

• cons
• nonn

Comments

Lampard dealt in a paper, see the links, with the calculation of internal cross capacitances of cylinders under certain conditions of symmetry. Van der Pauw generalized Lampard's results with the formula exp(-4*Pi^2*Cab,cd) + exp(-4*Pi^2*Cbc,da) = 1, see the links. Van der Pauw observed that in Lampard's case of symmetry, the two capacitances Cab,cd and Cbc,da are mutually equal, and hence are both equal to C = log(2)/(4*Pi^2) independently of the size or shape of the cross-section, which is Lampard's theorem.

Lampard's constant is closely related to Van der Pauw's constant A163973.

This constant was named after the Australian professor of electrical engineering Douglas Geoffrey Lampard (1927 - 1994). - Amiram Eldar, Dec 03 2020

Examples

			0.0175576231931707191...
		

Links

• D. G. Lampard, A new theorem in electrostatics with applications to calculable standards of capacitance, Proceedings of the IEE, Vol. 104, No. 6, pp. 271-280, September 1957.
• L. J. van der Pauw, A method of measuring specific resistivity and Hall effect of disc of arbitrary shape, Philips Research Reports, Vol. 13. no. 1, pp 1-9, February 1958.
• Index entries for transcendental numbers

Crossrefs

Cf. A163973 (Pi/log(2)), A118858 (log(2)/Pi^2), A000796 (Pi), A002162 (log(2)), A002388 (Pi^2), A092742 (1/Pi^2).

Programs

PARI

log(2)/(4*Pi^2) \\ Michel Marcus, Jul 04 2015

Formula

C = log(2)/(4*Pi^2).