We give a possible definition of 2-admissible functions (one possible generalization of Hayman-admissibility to bivariate functions) such that the coefficients of satisfy a central limit theorem. One typical example is , where the coefficients are the Stirling numbers of the second kind.

We also provide a list of closure properties of these kind of 2-admissible functions which can be automatically checked with the help of a MAPLE program.

Please send comments and corrections to Thomas Klausner.