Approximate Solution of Linear Differential Equations
The theory of linear differential equations is so powerful that one can usually predict the local behavior of the solutions near a point x 0 without knowing how to solve the differential equation. It suffices to examine the coefficient functions of the differential equation in the neighborhood of x 0.
KeywordsSingular Point Linear Differential Equation Leading Behavior Asymptotic Series Asymptotic Relation
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Chapter 3 For a general discussion see
Chapter 3 For asymptotic expansions of the special functions of mathematical physics and applied mathematics see Refs. 10 to 12 and
- 20.Watson, G. N., A Treatise on the Theory ofBessel Functions, 2d ed., Cambridge University Press, Cambridge, 1944.Google Scholar