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{\bf Strong asymptotics for relativistic Hermite polynomials}\\
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{\bf Wolfgang Gawronski (University of Trier, Germany)} \\
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\noindent
Recent investigations of the harmonic oscillator in the frame of relativistic
quantum theory lead to a wave equation the solution of which ''essentially''
is given by the relativistic Hermite polynomials $ H_n^N. $ Here $N$
denotes a positive parameter describing the relativistic effect such that
the system approaches the classical (nonrelativistic) model as $ N \to
\infty. $ This transition is made precise by the limiting relation \\
$$ \lim_{N \to \infty} \ H^N_n (x) = H_n (x) $$
\\
where $H_n$ denotes the well known Hermite polynomials. \\
\\
Most recent contributions are concerned with weak asymptotics that is the
asymptotic zero distribution for the relativistic Hermite polynomials
$ H^N_n. $ Extending and supplementing these results here we consider
strong asymptotics for the rescaled polynomials $ H^N_n (c_n x)
\ (c_n > 0 $ suitably, $ n, N \to \infty) $ that is Plancherel-Rotach
asymptotics. The proofs largely are based on corresponding results for
Jacobi polynomials with varying weights. \\


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