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Closed-form expressions for certain induction integrals involving Jacobi and Chebyshev polynomials. (English) Zbl 0941.65134
In the numerical solution of Cauchy singular integral equations (applied in airfoil theory, elasticity, and hydrodynamics) by collocation methods, certain non-singular mutual-induction integrals involving Jacobi and Chebyshev polynomials appear. However, the corresponding recursion scheme is seriously corrupted by numerical noise. The author shows that it is possible to derive closed-form expressions for these integrals that are free of such problems.

MSC:
65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type
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