This paper proposes the analytical non-compact Green's function utilizing the conformal transformation. Reviewing the Compact Green's function in the Theory of Vortex Sound suggests a new Green's function similar to the compact function. The two-dimensional Helmholtz equation in the new function replaces the Laplace's equation for the compact function. The variable separation method for solving the 2-D Helmholtz equation is revisited, which leads to the analytical solution composed of infinite series of the Bessel functions. Practically the solution of the scattered sound field around a circular cylinder is introduced using the series of the Bessel functions. The solution is applied to represent the analytical solution of the scattered sound field around 2-D boundary. For example, the scattered sound field around a flat strip or an airfoil is transferred from the sound field around a circular cylinder by using a reasonable mapping function. The validity of the new scattered sound field for a flat strip is examined with the contour of the equi-potential curves. The examination suggests utility of the new analytical function for the case of flat strip.
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