A further note on dual trigonometrical series

Abstract

This note discusses the determination of the coefficients an in the dual trigonometrical serieswhere p = ± 1 and F(x), G(x) are prescribed functions of X. It is shown that this problem and the corresponding one in which the sines in equations (1) are replaced by cosines are easily reduced to a form in which the results I have recently given in this journal [1] may be applied.As with my previous paper on this subject, the analysis is purely formal and no attempt is made to give precise conditions for which the solution is valid.