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In this article, we present the derivation of the asymptotic forms of theequations corresponding to the scattering coefficients of the exterior electricand magnetic fields of an infinite grating of insulating dielectric circularcylinders for vertically polarized and obliquely incident plane electromagneticwaves. Exploiting the generalized forms of the Twersky's elementary functionrepresentations for Schloemilch series, we have deducted an Ansatz describingthe behavior of the scattering coefficients of the electric and magnetic fieldsfor obliquely incident waves when the grating spacing is much smaller than thewavelength of the incident electromagnetic radiation. Introducing the statementof this Ansatz into the equations of the scattering coefficients of theinfinite grating at oblique incidence, and expanding the scatteringcoefficients in the form of an asymptotic series as a function of the ratio ofthe radius of the cylinders to the grating spacing, we have acquired two newinfinite sets of algebraic equations associated with the scatteringcoefficients of the exterior electric and magnetic fields of the grating forvertically polarized and obliquely incident plane waves.

On the Asymptotic Representation for Transverse Magnetic Multiple  Scattering of Radiation by an Infinite Grating of Dielectric Circular  Cylinders at Oblique Incidence