Abstract
We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for
large n and z, where z is a complex variable satisfying 0 arg z 12
π . A summary of the
asymptotic properties of Gn(ix) for real values of x and an approximation for its extreme zeros
as n→∞ are given. When the variables are such that z/n is finite, an expansion is obtained using
the method of steepest descents applied to a suitable integral representation. This expansion
holds everywhere in the first quadrant of the z -plane except in the neighbourhood of the point
z=in , where there is a coalescence of saddle points. Numerical results are presented to illustrate
the accuracy of the various expansions.
Original language | English |
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Pages (from-to) | 1-16 |
Number of pages | 16 |
Journal | Journal of Classical Analysis |
Volume | 1 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2012 |