No restrictions are made as to the multiplicity of either the roots of the characteristic equation or the roots of certain auxiliary characteristic equations, which are used in calculating the φ’s appearing in the characteristic polynomials.nIt is shown that in certain cases the solution y(x, ρ) (and its first n-1 derivatives) which satisfies the prescribed boundary conditions may be approximated, for large values of ρ in a suitable sector of the ρ-plane, by the solution z(x) (and its corresponding derivatives) of a certain lower order “degenerate equation.”
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