Affiliation:
1. University of Texas, Austin, Texas
Abstract
Many branches of mathematical physics use equations of the form[EQUATION]where λ is a small quantity, and the primes denote differentiation with respect to x. In the absence of a general solution, one tries to write f(x) as an expansion in powers of λ. More neatly, if[EQUATION]is tried, to fit the structure of (1), then the work reduces to the derivation of a series expansion for q(x). The solution is [1][EQUATION]where N signifies the order of approximation to which one wishes to go, and Y
2n
represents the member of order λ
2n
of a family of functions obtained by substitution of (3) into (1) and (2). The problem is to compute Y
2n
for as many values of n as possible.
Publisher
Association for Computing Machinery (ACM)
Reference3 articles.
1. J. A. Campbell "Computation of a Class of Functions Useful in the Phase-Integral Approximation - κ Results" to be published in J. Computational Physics. J. A. Campbell "Computation of a Class of Functions Useful in the Phase-Integral Approximation - κ Results" to be published in J. Computational Physics.
2. A FORTRAN-based list processor for Poisson series
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