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Integral representations for products of Airy functions ¶Part 3. Quartic products

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Abstract.

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.

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Authors and Affiliations

  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 3. Quartic products. Z. angew. Math. Phys. 48, 656–664 (1997). https://doi.org/10.1007/PL00001482

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  • DOI: https://doi.org/10.1007/PL00001482

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