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The kernels of the integral equations for scalar diffraction by strips and disks are special cases of a kernel connected with the generalized axially symmetrical wave equation. A transformation of this kernel enables the original singular integral equations to be reduced to Fredholm integral equations of the second kind. These can be solved asymptotically at high frequencies. Applications are made to diffraction by strips and disks with incident waves of arbitrary form. Special results involving diffraction of plane waves are recovered from the general formulas.