Summary
Convergence of a quadrature rule (described in a previous paper by the same authors) for the approximate evaluation of the Cauchy principal value integral
, where α, β>−1 and λ∈(−1, 1), is demonstrated for functionsf satisfying a Hölder condition of order one on [−1, 1].
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References
Elliott, D.: Uniform asymptotic expansions of the Jacobi polynomials and an associated function. Math. Comp.25, 309–315 (1971)
Lorentz, G. G.: Bernstein polynomials. Toronto, Canada: University of Toronto Press 1953
Muskhelishvili, N. I.: Singular, integral equations. Groningen, Holland: Noordhoff 1953
Paget, D. F., Elliott, D.: An algorithm for the numerical evaluation of certain Cauchy principal value integrals. Numer. Math.19, 373–385 (1972)
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Elliott, D., Paget, D.F. On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals. Numer. Math. 23, 311–319 (1974). https://doi.org/10.1007/BF01438258
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DOI: https://doi.org/10.1007/BF01438258