Closed-form representation for directivity of nonuniformly spaced linear arrays with arbitrary element patterns

A closed-form expression involving lambda functions is derived for the directivity of nonuniformly spaced symmetrical linear arrays which is valid for a wide variety of commonly used antenna elements. It is shown that this general expression for directivity reduces to the well-known classical result for a uniformly excited broadside array of isotropic sources with elements spaced a half-wavelength apart