Analytic Function Theory, Volume 1

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American Mathematical Soc., 1973 - Mathematics - 308 pages
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Emphasizes the conceptual and historical continuity of analytic function theory. This book covers canonical topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It also features chapters on majorization and on functions holomorphic in a half-plane.
  

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Contents

NUMBER SYSTEMS
1
THE COMPLEX PLANE
18
FRACTIONS POWERS AND ROOTS
46
HOLOMORPHIC FUNCTIONS
68
POWER SERIES
102
COMPLEX INTEGRATION
160
REPRESENTATION THEOREMS
196
THE CALCULUS OF RESIDUES
241
APPENDIX A Some Properties of Point Sets
277
On the Theory of Integration
288
BIBLIOGRAPHY
297
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Page 298 - Complex integration and Cauchy's theorem. (Cambridge Tracts in Mathematics and Mathematical Physics, No. 15.) Cambridge, University Press, 1914.

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