The spectral determinant for second order elliptic operators on the real line

We derive an expression for the spectral determinant of a second-order elliptic differential operator 𝒯 defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation 𝒯 u=0. Examples of application of the resulting formula include the explicit calculation of the determinant of harmonic and anharmonic oscillators with an added bounded potential with compact support.