Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions

A new representation for solutions of the one-dimensional Schrödinger equation −u″+q(x)u=ω2u is obtained in the form of a series possessing the following attractive feature. The truncation error is ω-independent for all ω∈R. For the coefficients of the series simple recurrent integration formulas are obtained which make the new representation applicable for computation.