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Zbl 0874.33004
Reid, W.H.
Integral representations for products of Airy functions. III: Quartic products. (English)
[J] Z. Angew. Math. Phys. 48, No.4, 656-664 (1997). ISSN 0044-2275; ISSN 1420-9039/e

[For Part II, see the author in ibid. 48, No. 4, 646-655 (1997; reviewed above).] \par Integral representations are obtained for some quartic products of the Airy functions $Ai(z)$ and $Bi(z)$. These integral representations are particularly useful in obtaining the constants which appear in the asymptotic expansions of their integrals. Some of these results are also relevant to the connection problem for the second Painlevé transcendent.
[Luigi Gatteschi (Torino)]

MSC 2000:: *33C10 Cylinder functions, etc.
34M55 Painlevé and other special equations
34E05 Asymptotic expansions (ODE)
44A15 Special transforms

Keywords: integral representations; asymptotic expansions; Airy functions

Citations: Zbl 0874.33003; Zbl 0824.33002

Cited in: Zbl 0874.33003

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