Abstract
The present paper presents a Gauss type quadrature formula for a Cauchy type integral whose density is the product of a Holder function by the weight function (1 − x) α (1 + x) β (Re α, Reβ > −1) of orthogonal Jacobi polynomials. It is shown that at the roots of the function of the second kind corresponding to the Jacobi polynomial P n (α,β) (x), the quadrature formula with n nodes gives the exact value of a Cauchy type integral for an arbitrary polynomial of order k ≤ 2n. This formula was tested when solving several contact and mixed problems of the theory of elasticity.
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