We agree with this opinion expressed by the giant of \; Diffraction. Fur thermore we think that SM and WH applied to the sa me problems (for instance the polygon diffraction) \; can determine a helpful synergy. In the pa st the SM and WH methods were considered disconnec ted in particular because the SM method was tradit ionally defined with the angular complex represent ation while the WH method was traditionally define d in the Laplace domain.

In this course we show that the two methods have sign ificant points of similarity when the representati on of problems in both methods are expressed in te rms of difference equations. The two methods show their diversity in the solution procedures that ar e completely different and effective. Both similar ity and diversity properties are of advantage in&n bsp\; &ldquo\;Progress and Prospects in The Theory of Linear Waves Propagation&rdquo\;.

< br>Moreover both methods have demonstrated t heir efficacy in studying particularly complex pro blems\, beyond the traditional problem of scatteri ng by a wedge: in particular the scattering by a t hree part polygon that we will present. Recent p rogress in both methods: One of the most relevant recent progress in SM is the derivation of functi onal difference equations without the use of Maliu zhinets inversion theorem.

One of the most relevant recent progress in WH is transfo rmation of WH equations into integral equations fo r their effective solution.

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