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• W2034331253 abstract "An automatic quadrature is presented for approximating Hadamard finite-part (fp) integrals of a smooth function, with a double pole singularity within the range of integration. The quadrature rule is derived from the differentiation of an approximation to a Cauchy principal value integral or the Hilbert transform. The approximation to the fp integral is represented as a function of the value of pole by using Chebyshev polynomials of the second kind. Since the error can be estimated independently of the value of pole, a set of integrals for a set of values of pole can be efficiently approximated to a required tolerance, with the same number of function evaluations. Numerical examples are also included to illustrate the performance of the methods." @default.
• W2034331253 created "2016-06-24" @default.
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• W2034331253 date "1994-05-01" @default.
• W2034331253 modified "2023-09-23" @default.
• W2034331253 title "Hilbert and Hadamard transforms by generalized Chebyshev expansion" @default.
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• W2034331253 doi "https://doi.org/10.1016/0377-0427(92)00003-r" @default.
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