A constructive method for plane-wave representations of special functions

A general constructive scheme for the derivation of plane-wave representations of special functions is proposed. Illustrative examples of the construction are given. As one case study, new integral representations of the elliptic Weierstrass ℘ function are derived; these complement, and generalize, similar new plane-wave integral representations of the same function recently found by Dienstfrey and Huang (2006) [8] using other techniques. Our approach is inspired by recent developments in the so-called Fokas transform for the solution of boundary value problems for partial differential equations.