Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence. Issue 3 (4th August 2020)

• Record Type: Journal Article
• Authors: Lekner, John
• Is Part Of: Quarterly journal of mechanics and applied mathematics. Volume 73:Issue 3(2020:Aug.)
• Page Start: 251
• Page End: 260
• Publication Date: 2020-08-04
• Subjects: Mechanics -- Mathematics -- Periodicals; Applied mathematics -- Periodicals; 530.1
• DOI: 10.1093/qjmam/hbaa010
• Languages: English
• ISSNs: 0033-5614

Abstract

Summary: Four distinct solutions exist for the potential distribution around two equal circular parallel conducting cylinders, charged to the same potential. Their equivalence is demonstrated, and the resulting analytical identities are discussed. The identities relate the Jacobi elliptic function $sn$, the Jacobi theta functions $\theta _1, ~\theta _2 $ and infinite series over trigonometric and hyperbolic functions.