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The Stokes phenomenon is studied with respect to an equation of Bessel type, and it is shown that the Stokes lines are associated with the cut in the complex plane required to make the complex exponential integral single-valued. The Stokes constant is derived by considering the continuity conditions at all points along a single Stokes line. Numerical examples are given for the calculation of Hankel functions and the roots of the Airy integrals and their derivatives. Applications to phase-integral theory and possible extensions to other equations are indicated.