A259679 - OEIS

%I #22 Dec 03 2020 06:58:29

%S 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,

%T 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,

%U 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

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

%C 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.

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

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

%H D. G. Lampard, <a href="http://dx.doi.org/10.1049/pi-c.1957.0032">A new theorem in electrostatics with applications to calculable standards of capacitance</a>, Proceedings of the IEE, Vol. 104, No. 6, pp. 271-280, September 1957.

%H L. J. van der Pauw, <a href="http://es.scribd.com/doc/44653007/1958-Van-Der-Pauw-Philips-Res-Rep-a-Method-of-Measuring-Specific-Resistivity-and-Hall-Effect-of-Discs-of-Arbitrary-Shape">A method of measuring specific resistivity and Hall effect of disc of arbitrary shape</a>, Philips Research Reports, Vol. 13. no. 1, pp 1-9, February 1958.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

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

%e 0.0175576231931707191...

%o (PARI) log(2)/(4*Pi^2) \\ _Michel Marcus_, Jul 04 2015

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

%K cons,nonn

%O 0,3

%A _Johannes W. Meijer_, Jul 03 2015