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Hille E. Pseudo-Poles in the Theory of Emden's Equation. Proc Natl Acad Sci U S A. 1972;69(5):1271-2doi: 10.1073/pnas.69.5.1271.
Hille, E. (1972). Pseudo-Poles in the Theory of Emden's Equation. Proceedings of the National Academy of Sciences of the United States of America, 69(5), 1271-2. https://doi.org/10.1073/pnas.69.5.1271
Hille, E. "Pseudo-Poles in the Theory of Emden's Equation." Proceedings of the National Academy of Sciences of the United States of America vol. 69,5 (1972): 1271-2. doi: https://doi.org/10.1073/pnas.69.5.1271
Hille E. Pseudo-Poles in the Theory of Emden's Equation. Proc Natl Acad Sci U S A. 1972 May;69(5):1271-2. doi: 10.1073/pnas.69.5.1271. PMID: 16591989; PMCID: PMC426679.
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Proc Natl Acad Sci U S A. 1972 May;69(5):1271-2. doi: 10.1073/pnas.69.5.1271.

Pseudo-Poles in the Theory of Emden's Equation.

Proceedings of the National Academy of Sciences of the United States of America

E Hille

Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, N.M. 87106.

PMID: 16591989 PMCID: PMC426679 DOI: 10.1073/pnas.69.5.1271

Abstract

It is known that Emden's equation y'' = x(1-m)y(m) has movable singularities where the solution becomes infinite for one-sided approach. If m = (p + 2)/p, p positive integer, the singularities look like poles of order p. In this note expansions in terms of powers and logarithms are obtained from which the nonpolar nature of these "pseudo-poles" becomes evident. Various extensions are considered. Convergence proofs are deferred to a more detailed publication.

References

  1. Proc Natl Acad Sci U S A. 1969 Jan;62(1):7-10 - PubMed

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