  This paper will demonstrate some new techniques for developing the theory of
Asian (arithmetic average) options pricing. We discuss the basic derivation of
the diffusion equations, and how various techniques from potential theory can
be applied to solve these complex expressions. The Whittaker-type confluent
hypergeometric functions are introduced, and we discuss how these functions are
related to other systems including Mehler-Fock and modified Bessel functions.
We close with a brief analysis of some index transforms and the kernels related
to these integral transforms.
