  In this article, we present the derivation of the asymptotic forms of the
equations corresponding to the scattering coefficients of the exterior electric
and magnetic fields of an infinite grating of insulating dielectric circular
cylinders for vertically polarized and obliquely incident plane electromagnetic
waves. Exploiting the generalized forms of the Twersky's elementary function
representations for Schloemilch series, we have deducted an Ansatz describing
the behavior of the scattering coefficients of the electric and magnetic fields
for obliquely incident waves when the grating spacing is much smaller than the
wavelength of the incident electromagnetic radiation. Introducing the statement
of this Ansatz into the equations of the scattering coefficients of the
infinite grating at oblique incidence, and expanding the scattering
coefficients in the form of an asymptotic series as a function of the ratio of
the radius of the cylinders to the grating spacing, we have acquired two new
infinite sets of algebraic equations associated with the scattering
coefficients of the exterior electric and magnetic fields of the grating for
vertically polarized and obliquely incident plane waves.
