Some new vanishing solutions of linear antenna synthesis problem according to prescribed amplitude radiation pattern

The synthesis problem of a linear antenna according to the given amplitude radiation pattern in the variational statement is considered. As a criterion of optimization the least-square deviation between the prescribed and obtained amplitude patterns is taken. The analytical vanishing solutions of Euler's equation are obtained. These solutions are presented as functions with complex parameters which are calculated easily from the set of transcendental equations. These solutions are better for such prescribed patterns which are vanishing too. Some numerical results are shown.