The hyperbolic–hypergeometric functions

In this work we present a new function to represent the approximate solution of a system of three charged particles. This function is based on an extension to two variables of the confluent hypergeometric function 1 F 1 of Kummer and can be obtained using a method similar to that used by Appell and Kampé de Fériet. We analyze the general properties of the function such as integral representations, series expansions, and asymptotic limits. We also show that the proposed functions verify a relation similar to that satisfied by the exponential and trigonometric–hyperbolic ones. A generalization to n-dimension is also presented. The mathematical properties of the functions indicate that they are suitable to be included in computation of electronic emission in collision processes.