PERTURBATIONS OF ZEROS OF SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIE

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Let P(z) and (P)(z) be polynomials of the same degree. We consider the equations u" =P(z)u and (u)" =(P)(z)(u) (z ∈ C) whose solutions are u(z) and (u)(z),respectively.Let zk(u) and zk((u)),k =1,2,…,be the zeros of u(z) and (u)(z),respectively.We derive bounds for the quantitysup j inf k[1/zk(u)-//zj((u))]
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