Macdonald's identities and integral representations of products of Airy functions

Abstract

In this paper, using the Macdonald's identities for the products of modified Bessel functions of first and second kinds, we derive new integral representations for the products of Airy functions and their derivatives. Manipulating the integrands of Macdonald's identities with various integral representations lead us to get new representations for the products of Airy functions and their derivatives.

Keywords:

• Bessel functions
• Macdonald's identities
• Laplace transform
• Airy function

AMS Classifications:

• 33C10
• 44A10

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Alireza Ansari http://orcid.org/0000-0003-4387-3779

Shiva Eshaghi http://orcid.org/0000-0003-2291-5968

Additional information

Funding

The first author would like to acknowledge Shahrekord University for financial support under grant 97GRN1M1328.