Power series for the parabolic cylinder function, Dv(z), are derived from known addition theorems, thus enabling a more compact and efficient expression of the function. One of the expansions is applied to find an asymptotic approximation for the function as mod v mod to infinity with mod...

We warn of a class of problems that occur when inverting some Characteristic Functions (CFs) which we term confluent. Confluences can arise in joint CFs during the derivation of the marginal density of some lower-dimensional combination of the components. We illustrate with a simple (yet common)...

Hypergeometric functions are a generalization of exponential functions. They are explicit, computable functions that can also be manipulated analytically. The functions and series we use in quantitative economics are all special cases of them. In this paper, a unified approach to hypergeometric...