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Greene, Robert Everist, 1943-

Function theory of one complex variable / Robert E. Greene, Steven G. Krantz. - 3rd ed. - xix, 504 pages : illustrations ; 26 cm. - Graduate studies in mathematics, v. 40 1065-7339 ; . - Graduate studies in mathematics, volume 40. .

Includes bibliographical references (pages 497-499) and index.

Contents 1 Fundamental concepts 1 2 Complex line integrals 29 3 Applications of the Cauchy integral 69 4 Meromorphic functions and residues 105 5 The zeros of a holomorphic function 157 6 Holomorphic functions as geometric mappings 179 7 Harmonic functions 207 8 Infinite series and products 255 9 Applications of infinite sums and products 279 10 Analytic continuation 299 11 Topology 335 12 Rational approximation theory 363 13 Special classes of holomorphic functions 385 14 Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings 415 15 Special functions 449 16 The prime number theorem 471 App. A Real analysis 487 App. B The statement and proof of Goursat's theorem 493

ISBN: 0821839624

LCCN: 2005057188

Subjects--Topical Terms:
Functions of complex variables.

LC Class. No.: QA331.7 / .G75 2006

Dewey Class. No.: