Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence. Issue 3 (4th August 2020) - Lekner, John
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 $θ _1, ~θ _2 $ and infinite series over trigonometric and hyperbolic functions.