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### Open Access Journals

CPAA

Mathematical justifications are given for several integral and
series representations of the Dirac delta function which appear in
the physics literature. These include integrals of products of
Airy functions, and of Coulomb wave functions; they also include
series of products of Laguerre polynomials and of spherical
harmonics. The methods used are essentially based on the
asymptotic behavior of these special functions.

DCDS-B

In this paper, we study the asymptotic behavior of the Hermite
polynomials $H_{n}((2n+1)^{1/2}z)$ as $n\rightarrow \infty$. A
globally uniform asymptotic expansion is obtained for $z$ in an
unbounded region containing the right half-plane Re $z \geq 0$. A
corresponding expansion can also be given for $z$ in the left
half-plane by using the symmetry property of the Hermite
polynomials. Our approach is based on the steepest-descent method
for Riemann-Hilbert problems introduced by Deift and Zhou.

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