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Alexandria already American Mathematical applied approach zero APPROXIMATE SOLUTION Approximating Polynomial arbitrary polynomial assumed assumption auxiliary theorem Bulletin closest coefficients conclusion constant multiple constant not depending continuity not exceeding continuous function convergence theorem corresponding denoted discussion dx L(Pn E. N. OBERG example existence and uniqueness f k(x follows Furthermore given function f(x Hence Holder's inequality hypothesis identical independent INTEGRAL EQUATIONS interval involving second derivatives Jackson June kernel Krawtchouk kx(x kz(x L(irn L(rn least less Let Pn(x linear Markoff's theorem Mathematical Society maximum McEwen mean value theorem method metodo minimizing minimum modulus of continuity n<rn NATHANIEL OBERG nomial paper Picone Poly polynomial pn(x positive constant possible Present problem proceed Professor proof qn(x rn—irn rn(x School similar SOLUTION OF INTEGRAL square a^x^b sufficient condition suitable summed t)uit)dt throughout tion Transactions Trn(x TTn(x University of Minnesota upper bound whence wth degree