A convergent expansion of the Airy's integral with incomplete Gamma functions

20 May 2020 Alvarez-Perez Jose Luis

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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  • CLASSICAL ANALYSIS AND ODES