The transmitted power coefficient of a harmonically oscillating Gaussian beam into the HE11 mode of a transverse offset weakly guiding fiber of step index profile is represented as an integral of the coupling power density over all the spectral components of the beam. This coupling of a complex power density into the fundamental mode of a fiber which takes into account the Fresnel losses is expressed in closed form by using a vectorial analysis: normal mode method, the field equivalence principle, the Lorentz reciprocity theorem and the translational addition expressions for the cylindrical functions. Numerical results of the transmitted power coefficient are presented for various normalized frequency parameter V, transverse offset R, and different launching distance d. ¿ American Geophysical Union 1996