The author discusses theoretical and computational aspects of the so- called Bickley functions
where is the modified Bessel function of the second kind. These functions arise in heat convection problems, neutron transport calculations, and in other fields. They can be represented in terms of a series of exponential integrals . The author thus investigates both these functions simultaneously. In particular he presents sharp bounds on for derives new uniform asymptotic expansions for and for and shows how the uniform expansion of can be used to start stable recurrence for sequences , , .