From the functional form of the author's definition, it looks like yes. However, to connect the two definitions probably requires using Cauchy's integral formu

From the functional form of the author's definition, it looks like yes. However, to connect the two definitions probably requires using Cauchy's integral formula (http://en.wikipedia.org/wiki/Cauchy%27s_integral_formula http://en.wikipedia.org/wiki/Cauchy%27s_integral_formula) and/or the complex method of residues, along with some line integral tricks (http://en.wikipedia.org/wiki/Methods_of_contour_integration http://en.wikipedia.org/wiki/Methods_of_contour_integration).