Abstract
The paper presents quadrature formulas for calculating integrals defined on the interval \((-1,1)\) and containing the Jacobi weight function \({\left({1-x}\right)^{\alpha}}{\left({1+x}\right)^{\beta}}\) . The exponents \(\alpha\) and \(\beta\) can be complex numbers that satisfy the condition \(\mathop{\textrm{Re}{\left[{\alpha},{\beta}\right]}}>-1\) . Different types of integrals such as regular, singular, and hypersingular integrals, as well as integrals with a logarithmic kernel are considered. The uniformity of quadrature formulas makes it possible to use them to solve integral equations containing an arbitrary combination of these integrals.
