On an Airy function of two variables Original Research Article

Let zC be a function of View the MathML source defined by View the MathML source Here C is a path of integration such that the integrand vanishes at its terminal points. This is called the Pearcey integral, and may be regarded as an Airy function of two variables. It is known that zC(x,y) satisfies a system of partial differential equations of the form View the MathML source View the MathML source equation(∗) View the MathML source which possesses the singularities x=∞ and y=∞ of irregular type. In the present paper, the asymptotic behavior of suitably chosen linearly independent solutions of (∗) near y=∞ is studied.