There are two main power series for the Airy functions, namely the Maclaurin and the asymptotic expansions. The former converges for all finite values of the complex variable, $z$, but it requires a large number of terms for large values of $|z|$, and the latter is a Poincar\'{e}-type expansion which is well-suited for such large values and where optimal truncation is possible... (read more)

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