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The Pauli and the Oberhettinger asymptotic expansions for the diffracted field produced by the scattering of a plane electromagnetic wave by a wedge are compared analytically and numerically, and their range of application is extended. The Pauli-Clemmow method of steepest descents is used to evaluate Sommerfeld's complex integral expression for the total field produced by the scattering of a plane electromagnetic wave by a perfectly conducting wedge. This method is applied in a manner somewhat different from that employed by Pauli and yields an asymptotic expansion which is simpler in form and of wider applicability than Pauli's original expression. This generalized form of Pauli's expansion can, for example, be applied to the computation of the fields diffracted by wedges which have exterior angles less than 180 degrees. It is shown that simply by rearranging the terms in this generalized Pauli expansion a generalized form of Oberhettinger's asymptotic expansion can be produced. The superiority of the generalized Pauli asymptotic expression over previously derived asymptotic expressions is demonstrated in numerical examples. These asymptotic expressions are used to obtain scalar diffraction coefficients which are valid in the transition regions at the shadow and reflection boundaries.