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AuthorPรณlya, George. author
TitleProblems and Theorems in Analysis II [electronic resource] : Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry / by George Pรณlya, Gabor Szegรถ
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998
Connect tohttp://dx.doi.org/10.1007/978-3-642-61905-2
Descript XII, 392 p. online resource

CONTENT

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. Rolleโ{128}{153}s Theorem and Descartesโ{128}{153} Rule of Signs -- 2. The Geometry of the Complex Plane and the Zeros of Polynomials -- 3. Miscellaneous Problems -- Six. Polynomials and Trigonometric Polynomials -- ยง 1 (1โ{128}{147}7) Tchebychev Polynomials -- ยง 2 (8โ{128}{147}15) General Problems on Trigonometric Polynomials -- ยง 3 (16โ{128}{147}28) Some Special Trigonometric Polynomials -- ยง 4 (29โ{128}{147}38) Some Problems on Fourier Series -- ยง 5 (39โ{128}{147}43) Real Non-negative Trigonometric Polynomials -- ยง 6 (44โ{128}{147}49) Real Non-negative Polynomials -- ยง 7 (50โ{128}{147}61) Maximum-Minimum Problems on Trigonometric Polynomials -- ยง 8 (62โ{128}{147}66) Maximum-Minimum Problems on Polynomials -- ยง 9 (67โ{128}{147}76) The Lagrange Interpolation Formula -- ยง 10 (77โ{128}{147}83) The Theorems of S. Bernstein and A. Markov -- ยง 11 (84โ{128}{147}102) Legendre Polynomials and Related Topics -- ยง 12 (103โ{128}{147}113) Further Maximum-Minimum Problems on Polynomials -- Seven. Determinants and Quadratic Forms -- ยง 1 (1โ{128}{147}16) Evaluation of Determinants. Solution of Linear Equations -- ยง 2 (17โ{128}{147}34) Power Series Expansion of Rational Functions -- ยง 3 (35โ{128}{147}43.2) Generation of Positive Quadratic Forms -- ยง 4 (44โ{128}{147}54.4) Miscellaneous Problems -- ยง 5 (55โ{128}{147}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 -- ยง 1 (1โ{128}{147}25) Some Geometric Problems -- Errata -- ยง 1 Additional Problems to Part One -- New Problems in English Edition -- Author Index -- Topics


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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