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

  • W. H. Reid
Article

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.

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

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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

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

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