This paper presents a method for translating an asymptotic expansion of a function around a dominant singularity into an asymptotic expansion for the Taylor coefficients of the function. The approach is based on contour integration using Hankel and Cauchy's formula, offering an alternative to Darboux's method or Tauberian theorems. It is particularly useful for combinatorial enumerations and provides a general framework for analyzing the asymptotic behavior of coefficients of functions with a unique dominant singularity. The paper includes detailed proofs and examples to illustrate the application of these transfer theorems, including extensions to functions with logarithmic and iterated logarithmic terms. The results are organized into sections covering basic transfer theorems, extensions to larger functions and slowly varying functions, and a comparison with alternative methods such as Darboux's method and Tauberian theorems.This paper presents a method for translating an asymptotic expansion of a function around a dominant singularity into an asymptotic expansion for the Taylor coefficients of the function. The approach is based on contour integration using Hankel and Cauchy's formula, offering an alternative to Darboux's method or Tauberian theorems. It is particularly useful for combinatorial enumerations and provides a general framework for analyzing the asymptotic behavior of coefficients of functions with a unique dominant singularity. The paper includes detailed proofs and examples to illustrate the application of these transfer theorems, including extensions to functions with logarithmic and iterated logarithmic terms. The results are organized into sections covering basic transfer theorems, extensions to larger functions and slowly varying functions, and a comparison with alternative methods such as Darboux's method and Tauberian theorems.