A Note on biharmonic functions

Abstract

The condition that four complex functions φ₁ (z), φ₂ (z), ψ₁ (z), ψ₂ (z̄) are two pairs of mutually conjugate ones ${{\phi }_{2}}\left( {\bar{z}} \right) = \overline {{{\phi }_{1}}\left( z \right),} {\kern 1pt} {{\psi }_{2}}\left( {\bar{z}} \right) = \overline {{{\psi }_{1}}\left( z \right)}$ to be a real function. This paper presents a necessary and sufficient condition.