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.

中文翻译：

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麦克唐纳恒等式和艾里函数乘积的积分表示

在本文中，使用第一类和第二类修正 Bessel 函数的乘积的 Macdonald 恒等式，我们推导出了 Airy 函数及其导数的乘积的新积分表示。使用各种积分表示来操纵 Macdonald 恒等式的被积函数使我们获得了 Airy 函数及其导数的乘积的新表示。