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Introduction to complex analysis. Part 1: Functions of one variable. Textbook. (Vvedenie v kompleksnyj analiz. Chast’ 1: Funktsii odnogo peremennogo. Uchebnoe posobie). 3rd ed., rev. and compl. (Russian) Zbl 0574.30001
Moskva: ”Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 336 p. R. 0.95 (1985).
The first edition of this textbook (1969; Zbl 0188.379) consists of two parts (published together in one volume), devoted to I. Function theory of one complex variable and II. Function theory of several complex variables.
In this third revised and completed edition (as well as in the second one), the two parts are published separately. In the first part (under review), there are some changes in the paragraphs on analytic continuation and the growth of entire functions and also some new sections devoted to algebraic functions, elliptic functions and Kotel’nikov’s theorem on an interpolation formula for entire functions. In order to fix better the results in the student’s mind, the author introduces some exercises in the text and at the end of the chapters.
Finally, he inserts also historical informations with respect to the fundamental concepts of complex analysis, which are taken from the paper ”Analytic function theory” of A. I. Markushevich [chapter 2 in ”Mathematics of the XIX-th century” (Russian) Moscow, Nauka (1981)].
Reviewer: P.Caraman

30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable