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＜E-Book＞
Problems and Theorems in Analysis II : Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry / by George Polya, Gabor Szegö
(Classics in Mathematics. ISSN:25125257)

Edition	1st ed. 1998.
Publisher	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Year	1998
Language	English
Size	XII, 392 p : online resource
Authors	*Polya, George author Szegö, Gabor author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis FREE:Analysis
Notes	Four. Functions of One Complex Variable. Special Part -- 1. Maximum Term and Central Index, Maximum Modulus and Number of Zeros -- 2. Schlicht Mappings -- 3. Miscellaneous Problems -- Five. The Location of Zeros -- 1. Rolle’s Theorem and Descartes’ Rule of Signs -- 2. The Geometry of the Complex Plane and the Zeros of Polynomials -- 3. Miscellaneous Problems -- Six. Polynomials and Trigonometric Polynomials -- § 1 (1–7) Tchebychev Polynomials -- § 2 (8–15) General Problems on Trigonometric Polynomials -- § 3 (16–28) Some Special Trigonometric Polynomials -- § 4 (29–38) Some Problems on Fourier Series -- § 5 (39–43) Real Non-negative Trigonometric Polynomials -- § 6 (44–49) Real Non-negative Polynomials -- § 7 (50–61) Maximum-Minimum Problems on Trigonometric Polynomials -- § 8 (62–66) Maximum-Minimum Problems on Polynomials -- § 9 (67–76) The Lagrange Interpolation Formula -- § 10 (77–83) The Theorems of S. Bernstein and A. Markov -- § 11 (84–102) Legendre Polynomials and Related Topics -- § 12 (103–113) Further Maximum-Minimum Problems on Polynomials -- Seven. Determinants and Quadratic Forms -- § 1 (1–16) Evaluation of Determinants. Solution of Linear Equations -- § 2 (17–34) Power Series Expansion of Rational Functions -- § 3 (35–43.2) Generation of Positive Quadratic Forms -- § 4 (44–54.4) Miscellaneous Problems -- § 5 (55–72) Determinants of Systems of Functions -- Eight. Number Theory -- 1. Arithmetical Functions -- 2. Polynomials with Integral Coefficients and Integral-Valued Functions -- 3. Arithmetical Aspects of Power Series -- 4. Some Problems on Algebraic Integers -- 5. Miscellaneous Problems -- Nine. Geometric Problems -- § 1 (1–25) Some Geometric Problems -- Errata -- § 1 Additional Problems to Part One -- New Problems in EnglishEdition -- Author Index -- Topics HTTP:URL=https://doi.org/10.1007/978-3-642-61905-2

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