UID:
almahu_9947366614902882
Format:
1 online resource (237 pages)
ISBN:
1-281-76363-2
,
9786611763633
,
0-08-087371-5
Series Statement:
Pure and applied mathematics ; 56
Note:
Description based upon print version of record.
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Front Cover; Introduction to the Theory of Entire Functions; Copyright Page; Contents; Preface; Chapter I. A Study of the Maximum Modulus and Basic Theorems; 1.1 The Nature of Singular Points; 1.2 Meromorphic Functions (Definition); 1.3 Entire Functions (Definition); 1.4-1.8 Maximum and Minimum Modulus; 1.9 Order of Zeros; 1.10 Algebraic Entire Functions; 1.11 Rate of Increase of Maximum Modulus and Definition of Order; 1.12 The Disjunction of Zeros of a Nonconstant Entire Function; 1.13-1.14 Fundamental Properties of the Complex Number System: Elementary Theorems on Zeros of Entire Functions
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1.15 Hadamard's Three-Circle Theorem and Convexity; 1.16 Infinite Products; Chapter II. The Expansion of Functions and Picard Theorems; 2.1 Residues; 2.2-2.3 Expansion of a Meromorphic Function; 2.4 Expansion of an Entire Function; 2.5 Rouché's Theorem; 2.6 Hurwitz's Theorem; 2.7 Picard Theorems for Functions of Finite Order; Chapter III. Theorems Concerning the Modulus of a Function and Its Zeros; 3.1 Inequalities for R {f(z)}; 3.2 Poisson's Integral Formula; 3.3 Jensen's Theorem; 3.4 The Poisson-Jensen Formula; 3.5 Carleman's Theorem; 3.6 Schwarz's Lemma
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3.7 A Theorem of Borel and Carathéodory; Chapter IV. Infinite Product Representation: Order and Type; 4.1 Weierstrass Factorization Theorem; 4.2 Order of an Entire Function; 4.3 Type of an Entire Function; 4.4 Growth of f(z) in Unbounded Subdomains of the Plane; 4.5-4.6 Enumerative Function n(r); 4.7 Exponent of Convergence; 4.8 Genus of a Canonical Product; 4.9 Hadamard's Factorization Theorem; 4.10 Order and Exponent of Convergence; 4.11 Genus of an Entire Function; 4.12-4.13 Order and Type of an Entire Function Defined by Power Series
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4.14 On an Entire Function of an Entire Function (G . Pólya); Chapter V. Standard Functions and Characterization Theorems; 5.1 The Gamma Function; 5.2 Analytic Continuation of ?(z); 5.3 Conjugate Points; 5.4 Bessel's Function; 5.5 The Function Fa(z) = exp(-ta) cos zt dt (a 〉 1); 5.6 Order of the Derived Function; 5.7 Laguerre's Theorem; 5.8 Convex Sets and Lucas's Theorem; 5.9-5.10 Mittag-Leffler Theorem; Chapter VI. Functions with Real and/or Negative Zeros: Minimum Modulus I and Sequences of Functions; 6.1 Functions with Real Zeros Only; 6.2 The Minimum Modulus m(r)
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6.3 Sequences of Functions; 6.4 Vitali's Convergence Theorem; 6.5 Montel's Theorem; Chapter VII. Theorems of Phragmén and Lindelöf: Minimum Modulus II; 7.1-7.7 Theorems of Phragmén and Lindelöf; 7.8 The Indicator Function h(F); 7.9 Behavior of m(r); Chapter VIII. Theorems of Borel, Schottky. Picard, and Landau: Asymptotic Values; 8.1 a-Points of an Entire Function; 8.2 Borel's Theorem; 8.3-8.5 Exceptional-B Values; 8.6 Exceptional-P Values; 8.7 Schottky's Theorem; 8.8 Picard's First Theorem; 8.9 Landau's Theorem; 8.10 Picard's Second Theorem; 8.11 Asymptotic Values; 8.12 Contiguous Paths; Chapter IX. Elementary Nevanlinna Theory
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English
Additional Edition:
ISBN 0-12-352750-3
Language:
English
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