Some results involving integral transforms of Airy functions

Abstract

In this paper, using the Schouten–Vanderpol and Titchmarsh theorems for the inverse Laplace transform, we obtain new integral identities for the Airy functions and their products. These integral identities are given in terms of the Laplace, Stieltjes and Hankel transforms.

Keywords:

• Airy functions
• Laplace transform
• Stieltjes transform
• Hankel transform

Mathematics Subject Classifications:

• 33C
• 44A

Acknowledgments

The authors wishes to thank referees for constructive comments and suggestions. Also, they would like to thank Dr N. Ahanjideh for reading the final version of paper.

Disclosure statement

No potential conflict of interest was reported by the authors.