On Some Integral Equations with a Hankel Function Kernel

A method is presented for converting integral and integro-differentialequations whose kernel is the Hankel function into Cauchy singular equations. The latter may be solved bystandard function-theoretic methods or by implementing a secondtransformation to convert them into Abel-type equations, whichare readily inverted. Examples are drawn from wave diffractiontheory in two dimensions and include a mixed boundary-valueproblem which may be reduced to a pair of coupled integro-differentialequations. It is shown that the conversion to a singular equationpair and thence to Abel form permits uncoupling and a directsolution. Other applications of the method are briefly indicated.