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a.p. function apolar apolar pair axis belonging Bessel functions boundary closed interval closed set coefficients cone conic consider constant contact transformation containing continued fraction core corresponding cosh kz cubic curve cubic surface deduce defined degree denote derivative envelope equal equation exists exponents expression F-curve field-point fixed follows formula Fourier series G. H. Hardy given Hence Hessian Hessian pencil identity inequality integrand intersection J. E. Littlewood Lemma lim inf limit linear Littlewood London Math method multiple negative null series obtain parameters polar line poles polynomials positive integer positive number Proc proof of Theorem proved quadric quartic quartic surface quintic curves residual respect result satisfies Satz sequence sextic Similarly solution straight lines suppose tangent planes theory tion touch twisted cubic uniformly convergent values variables W. H. Young Watson zero mass