Abstract
For second order equations -(py1)1 + qy = λy on [0,∞) it is known that the Titchmarsh—Wey1 coefficient m(λ) for large |λ| is asymptotically equivalent to that of the Fourier equation -y” = λy. There is at present no corresponding result for fourth order equations. In this paper we construct the ij (λ) coefficients for the fourth order equation y(4)—((x2 + 4k)y')'—¼y = λy on [O, ∞) explicitly in terms of Integrals of Whittaker functions. We show that as |λ|→∞ the coefficients approach those of the corresponding Fourier equation y(4) = λy.