Abstract
Exact analytical solutions of certain second-order linear differential equations are often employed as approximate solutions of other second-order differential equations when the solutions of this latter equation cannot be expressed in terms of the standard transcendental functions. The classical exposition of this method has been given by Jeffreys (6); approximate solutions of the equation (using Jeffreys's notation)are given in terms of solutions either of the equationor of the equationwhere h is a large parameter. A complete history of this technique is given in the author's recent text An introduction to phase-integral methods (Heading (5)).
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