## A Boundary Value Problem Involving an Exponential Turning Point |

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abbreviate American Mathematical Analagous results arbitrary function assumption that q(x asymptotic forms becomes large Bessel's boundary problem BOUNDARY VALUE PROBLEM bounded from zero bounded function bounded variation Characteristic Equation characteristic functions characteristic values circle Consider Convergence Theorems converges to zero critical point Degree of Doctor diameter joining differential equation Expansion Problems EXPONENTIAL TURNING POINT func Green's Function half-plane Hence independent solutions infinite order integral interior point interlaced infinite sets interval a,a INVOLVING AN EXPONENTIAL istic Langer lemma manner we show Montana Academy odd function order higher Ordinary Differential pansion Partial Fulfillment Real Variable right hand side Robert Edward Lowney roots satisfies segments self-adjoint semicircle sense of Lebesgue series of characteristic shown similar discussion similar manner stant sufficiently large tangents terval theorem is proved theory Thesis Submitted uniformly bounded University of Wisconsin usual process VALUE PROBLEM INVOLVING vanish whence wherein