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Sources in the development of mathematics infinite series and products from the fifteenth to the twenty-first century

Ranjan Roy 1948-

2011

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  • Title:
    Sources in the development of mathematics infinite series and products from the fifteenth to the twenty-first century
  • Author: Ranjan Roy 1948-
  • Description: Cover; Title; Copyright; Contents; Preface; 1 Power Series in Fifteenth-Century Kerala; 1.1 Preliminary Remarks; 1.2 Transformation of Series; 1.3 Jyesthadeva on Sums of Powers; 1.4 Arctangent Series in the Yuktibhasa; 1.5 Derivation of the Sine Series in the Yuktibhasa; 1.6 Continued Fractions; 1.7 Exercises; 1.8 Notes on the Literature; 2 Sums of Powers of Integers; 2.1 Preliminary Remarks; 2.2 Johann Faulhaber and Sums of Powers; 2.3 Jakob Bernoulli's Polynomials; 2.4 Proof of Bernoulli's Formula; 2.5 Exercises; 2.6 Notes on the Literature; 3 Infinite Product of Wallis
    3.1 Preliminary Remarks3.2 Wallis's Infinite Product for bold0mu mumu Raw; 3.3 Brouncker and Infinite Continued Fractions; 3.4 Stieltjes: Probability Integral; 3.5 Euler: Series and Continued Fractions; 3.6 Euler: Products and Continued Fractions; 3.7 Euler: Continued Fractions and Integrals; 3.8 Sylvester: A Difference Equation and Euler's Continued Fraction; 3.9 Euler: Riccati's Equation and Continued Fractions; 3.10 Exercises; 3.11 Notes on the Literature; 4 The Binomial Theorem; 4.1 Preliminary Remarks; 4.2 Landen's Derivation of the Binomial Theorem
    4.3 Euler's Proof for Rational Indices4.4 Cauchy: Proof of the Binomial Theorem for Real Exponents; 4.5 Abel's Theorem on Continuity; 4.6 Harkness and Morley's Proof of the Binomial Theorem; 4.7 Exercises; 4.8 Notes on the Literature; 5 The Rectification of Curves; 5.1 Preliminary Remarks; 5.2 Descartes's Method of Finding the Normal; 5.3 Hudde's Rule for a Double Root; 5.4 Van Heuraet's Letter on Rectification; 5.5 Newton's Rectification of a Curve; 5.6 Leibniz's Derivation of the Arc Length; 5.7 Exercises; 5.8 Notes on the Literature; 6 Inequalities; 6.1 Preliminary Remarks
    7.10 Exercises7.11 Notes on the Literature; 8 The Calculus of Newton and Leibniz; 8.1 Preliminary Remarks; 8.2 Newton's 1671 Calculus Text; 8.3 Leibniz: Differential Calculus; 8.4 Leibniz on the Catenary; 8.5 Johann Bernoulli on the Catenary; 8.6 Johann Bernoulli: The Brachistochrone; 8.7 Newton's Solution to the Brachistochrone; 8.8 Newton on the Radius of Curvature; 8.9 Johann Bernoulli on the Radius of Curvature; 8.10 Exercises; 8.11 Notes on the Literature; 9 De Analysi per Aequationes Infinitas; 9.1 Preliminary Remarks; 9.2 Algebra of Infinite Series; 9.3 Newton's Polygon
    9.4 Newton on Differential Equations
    A look at the discovery and use of infinite series and products from Wallis and Newton through Euler and Gauss to the present day.
  • Publication Date: 2011
  • Publisher: Cambridge ; New York : Cambridge University Press
  • Format: 1 online resource (996 p.).
  • Identifier: ISBN 1-316-08658-5;ISBN 1-139-63551-4;ISBN 1-283-29584-9;ISBN 1-139-12260-6;ISBN 9786613295842;ISBN 0-511-84419-0;ISBN 1-139-11686-X;ISBN 1-139-12752-7;ISBN 1-139-11250-3;ISBN 1-139-11469-7
  • Subjects: Mathematics -- Historiography; Infinite; Electronic books
  • Language: English
  • Source: 01DAL UDM ALMA

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