A series of “cut” Bessel functions

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Abstract
In Kottler's theoretical discussion1 of the diffraction of a plane wave of monochromatic light of wave-length 2π/k by a black halfplane, the functionwhere (r, θ, z) are cylindrical coordinates, plays an important part. In particular it is necessary to have asymptotic formulae for f (r, θ), valid when r is either very large or very small compared with the wave-length.

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