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This paper presents an overview of several integral equation (IE) formulations where the use of Legendre basis functions is beneficial. Specifically, we introduce the basis functions and deal with formulations for surface IE, volume IE, volume-surface IE, and layered media, respectively. In some cases, the high complexity of a problem arises due its large size in terms of wavelengths which can be handled with the MoM-PO approach described. Finally, we present a numerical example solved with two different formulations.