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Zbl 0695.33007
Smith, Donald R.
A Riccati approach to the Airy equation. (English)
[A] Asymptotic and computational analysis. Conference in honor of Frank W.J. Olver's 65th birthday, Proc. Int. Symp., Winnipeg/Can. 1989, Lect. Notes Pure Appl. Math. 124, 403-415 (1990).

[For the entire collection see Zbl 0689.00009.] \par In earlier papers, the author has shown that by using a Riccati transformation it can be obtained the approximate solution of the Airy equation $f''(z)=zf(z)$ on the real axis. In the present paper, this transformation is used for a study of the Airy equation for complex z, in particulary in the region $\vert ph(z)\vert \le \pi /3$ and in other regions of the complex plane, too.
[St.Kus]

MSC 2000:: *33C10 Cylinder functions, etc.
34M99 Differential equations in the complex domain

Keywords: Airy function; Riccati transformation; Airy equation

Citations: Zbl 0689.00009

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