Generalization of Fock function for diffraction by elongated bodies

High-frequency asymptotics of electromagnetic field diffracted by an elongated body is constructed in the form similar to well known V. A. Fock asymptotics, where instead of Fock function a new special function A(η, ω) appears. The first argument η defines the point on the surface and the second ω characterizes the rate of elongation. The function A(η, ω) is given in the form of an integral of an expression containing Coulomb wave functions. For large ω special function A(η, ω) reduces asymptotically to Fock function. For small ω comparison with numerical results provided by M. Duruflé (Institut de Mathmatiques de Bordeaux, France) show good accuracy of the asymptotic formula in all test examples.