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Integral Equations Satisfied by Lamé-Wangerin Functions

Published online by Cambridge University Press:  20 January 2009

C. G. Lambe
Affiliation:
Militaby College of Science, Shbivenham.
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Summary

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Integral equations are obtained with nuclei (l — zt/a)2n and (z–t)2n which are satisfied by characteristic solutions of the transformed Lamé-Wangerin equation of order n, and each of the two characteristic solutions is expressed in terms of the other by a contour integral.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

Page 71 note 1 Halphen, G. H., Traité des Fonctioni Elliptiques (Paris, 1888), t.2, p. 471.Google ScholarWhittaker and Watson, Modern Analysis (Cambridge, 1920, 3rd ed.), §§ 23–7.Google Scholar

Page 72 note 1 Lambé, C. G. and Ward, D. R., Quart. J. of Math. (Oxford), 5 (1934), 81Google Scholar and Erdélyi, A., Quart. J. Math. (Oxford), 13 (1942), 107.Google Scholar