Abstract

An integral equation is called singular if either the range of integration is infinite or the kernel has singularities within the range of integration. Such equations occur rather frequently in mathematical physics and possess very unusual properties. This chapter discusses singular integral equations, Cauchy principal value for integrals, and the solution of the cauchy-type singular integral equation. A kernel of the form [K(s,t) = cot(t-s)/2], where s and t are real variables, is called the Hilbert kernel and is closely connected with the Cauchy kernel. The chapter also discusses how the Hilbert kernel is also related to the Poisson kernel.

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