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Asymptotic formulae for solutions of linear second-order differential equations with a large parameter
Published online by Cambridge University Press: 09 April 2009
Abstract
Uniform asymptotic formulae are obtained for solutions of the differential equation for large positive values of the parameter u. Here p is a positive integer, θ an arbitrary parameter and z a complex variable whose domain of variation may be unbounded. The function ƒ (u, θ, z) is a regular function of ζ having an asymptotic expansion of the form for large u.
The results obtained include and extend those of earlier writers which are applicable to this equation.
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- Copyright © Australian Mathematical Society 1960
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