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Zbl 0874.33003
Reid, W.H.
Integral representations for products of Airy functions. II: Cubic products. (English)
[J] Z. Angew. Math. Phys. 48, No.4, 646-655 (1997). ISSN 0044-2275; ISSN 1420-9039/e

[For Part I see the author in ibid. 46, No. 2, 159-170 (1995; Zbl 0824.33002).] \par Integral representations are obtained for some cubic products of the Airy functions $Ai(z)$ and $Bi(z)$. These integral representations are of the Laplace contour type but they involve the modified Bessel functions of order $\frac{1}{6}$. From these results it is possible to evaluate a number of definite integrals involving such cubic products.
[Luigi Gatteschi (Torino)]

MSC 2000:: *33C10 Cylinder functions, etc.
34M99 Differential equations in the complex domain
34E05 Asymptotic expansions (ODE)
44A15 Special transforms

Keywords: integral representations; asymptotic expansions; Airy functions; Bessel functions

Citations: Zbl 0874.33004; Zbl 0824.33002

Cited in: Zbl 0874.33004

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