On the completeness of the system of function {e sin λnx}n = 1

In this paper, the biorthogonal system corresponding to the system {e^−αnx sin nx}_{n = 1}^∞ is represented in an appropriate form so that it is possible to obtain sufficiently good estimates of its norm. Then, by the stability of a completeness property we prove that the system of functions {e^−αλ_nx sin λ_nx}_{n = 1}^∞ is complete.