ABSTRACT
As a preliminary to the consideration of series of fractions (Sections 1.2 and 1.3), infinite products (Sections 1.4 and 1.5), and continued fractions (Sections 1.6 through 1.9), some properties of complex functions (Chapters I.21, 23, 25, 27, and 29) are briefly reviewed concerning: (1) the Taylor (Laurent) series [Subsection 1.1.1 (Subsection 1.1.2)] around a regular point (isolated singularity); (2) the classification of singularities [Subsection 1.1.3 (Subsection 1.1.5)] in the finite plane (at infinity); (3) the classification of functions from their singularities (Subsection 1.1.6); (4) the calculation of the coefficients of the principal part near a pole including the residue (Subsection 1.1.4); (5) the integral (meromorphic) functions [Subsection 1.1.7 (Subsection 1.1.10)] as extensions of polynomials (rational
functions), with the primary (secondary) circular functions as examples [Subsection 1.1.8 (Subsection 1.1.11)]; and (6) the rational-integral and polymorphic functions (Subsection 1.1.9) to complete the classification of functions. The subject matter of Volume II thus starts with Section 1.2.
