The asymptotic form of the Titchmarsh-Weyl m-coefficient for the differential equation −(py′)′+q j = λwy on [a, b). (′≡d/dx), as |λ|→∞, is obtained under general conditions on the real-valued coefficients p, q and w, with p≧0 and w≧0. Examples are given to show that the result is near to but possible, although there are many interesting cases for which the asymptotic form of the m-coefficient is still not known.
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Everitt et al. (1978) studied this question.