Generalized Noninterpolatory Rules for Cauchy Principal Value Integrals
نویسنده
چکیده
Consider the Cauchy principal value integral I(kf;X)=i k{x)F^Ldx, -1<A<1. 7-1 x — A If we approximate f(x) by Yli=oajP¡(x'i w) where {p } is a sequence of orthonormal polynomials with respect to an admissible weight function w and û, = (/. P.), then an approximation to I(kf; X) is given by X!/=o ajl(kp¡ ; ^)If, in turn, we approximate a¡ by ajm = £TM , wimf(x¡m)Pj(xim), then we get a double sequence of approximations {Qm(f;X)} to I(kf; X). We study the convergence of this sequence by relating it to the sequence of approximations associated with l(wf ; X) which has been investigated previously.
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