The Sommerfeld identity is a mathematical identity, due Arnold Sommerfeld, used in the theory of propagation of waves, where is to be taken with positive real part, to ensure the convergence of the integral and its vanishing in the limit and . Here, is the distance from the origin while is the distance from the central axis of a cylinder as in the cylindrical coordinate system. Here the notation for Bessel functions follows the German convention, to be consistent with the original notation used by Sommerfeld. The function Where [Ref.2,Pg.66]. The notation used here is different form that above: . , , or , .