Higher Monotonicity Properties of Certain Sturm-Liouville Functions. IV

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Abstract
The Sturm-Liouville functions considered in this instalment are real (as are all other quantities discussed here) non-trivial solutions of the differential equation 1.1 Higher monotonicity properties, as defined in § 2, are investigated for a number of sequences (finite or infinite) associated with these functions. One such sequence, discussed in detail later, has the kth term 1.2 where the constant X > — 1 (to assure convergence of each integral), W(x) possesses higher monotonicity properties and, moreover, is such that, again, each integral converges, and X1, X2, … is a sequence (finite or infinite) of consecutive zeros of a solution of (1.1), which may or may not be linearly independent of y(x), in the interval of definition of the functions under consideration.

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