Integral representations for products of Airy functions ¶Part 2. Cubic products

Abstract.

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 \(\frac 16\). From these results it is then possible to evaluate a number of definite integrals involving such cubic products.

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1. Dept. of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, Indiana, 46202-3216, USA, (Fax: 317-274-3460), USA

   W. H. Reid

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1. W. H. Reid
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Received: June 13, 1996

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Reid, W. Integral representations for products of Airy functions ¶Part 2. Cubic products. Z. angew. Math. Phys. 48, 646–655 (1997). https://doi.org/10.1007/PL00001481

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• Published: 01 July 1997

• Issue Date: July 1997

• DOI: https://doi.org/10.1007/PL00001481

• Key words. Airy functions, integral representations, asymptotic expansions.