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The Quarterly Journal of Mechanics and Applied Mathematics 1967 20(3):365-380; doi:10.1093/qjmam/20.3.365
© 1967 by Oxford University Press
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UNIFORM ASYMPTOTIC FORMS OF MODIFIED MATHIEU FUNCTIONS

ALAN SHARPLES

( Department of Mathematics, University of Manchester )

Asymptotic forms are derived for the functions and their derivatives in terms of elementary functions and Airy functions respectively. They are uniformly valid with respect to arg v and all values of the complex variable z which lie in an open, simply-connected unbounded domain, when is large.


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