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OverviewA remarkable interplay exists between the fields of elliptic functions and orthogonal polynomials. In the first monograph to explore their connections, Elliptic Polynomials combines these two areas of study, leading to an interesting development of some basic aspects of each. It presents new material about various classes of polynomials and about the odd Jacobi elliptic functions and their inverses. The term elliptic polynomials refers to the polynomials generated by odd elliptic integrals and elliptic functions. In studying these, the authors consider such things as orthogonality and the construction of weight functions and measures, finding structure constants and interesting inequalities, and deriving useful formulas and evaluations. Although some of the material may be familiar, it establishes a new mathematical field that intersects with classical subjects at many points. Its wealth of information on important properties of polynomials and clear, accessible presentation make Elliptic Polynomials valuable to those in real and complex analysis, number theory, and combinatorics, and will undoubtedly generate further research. Full Product DetailsAuthor: J.S. Lomont , John BrillhartPublisher: Taylor & Francis Ltd Imprint: Chapman & Hall/CRC Weight: 0.453kg ISBN: 9780367398200ISBN 10: 0367398206 Pages: 320 Publication Date: 23 September 2019 Audience: College/higher education , General/trade , Tertiary & Higher Education , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction; Binomial Sequences of Polynomials; The Set of Functions F; The Set of Functions F0. The Sequences {Gm(z)} and {Hm(z)}; The Binomial Sequence Derived from ƒ-1, where ƒ F0;The Set of Functions F1 Elliptic Integrals and Polynomials of the First Kind; The Moment Polynomials Pn(x,y), Qn(x,y), and Rn(x,y); The Set of Functions F1-1; Elliptic Functions and Polynomials of the Second Kind; Inner Products, Integrals, and Moments. Favard's Theorem; The Set of Functions F2. The Orthogonal Sequences {Gm(z)} and {Hm(z)}; Class I Functions. Class II Functions, Tangent Numbers, Class III Functions: The Modified Mittag-Leffler Polynomial n(x). Structure Constants; The Coefficients of the n(x) Polynomials, The n(x) Polynomials, The Orthogonal Sequences {Am(z)} and {Bm(z)} . Structure Constants; Weight Functions for the Sequences {Am(z)} and {Bm(z)}; Miscellaneous Results, Uniqueness and Completion Results, Polynomial Inequalities, Some Concluding QuestionsReviewsThe book under review has several unusual features. Particularly striking is the interplay among mathematical topics for which few connections had been previously noticed. The connection between orthogonal polynomials and their properties with elliptic functions should be valuable to those working in elliptic function. accessible to a wide variety of mathematicians and students of mathematics. The book serves as an excellent introduction to such topics as orthogonal polynomials, elliptic integrals, and the study of polynomials in general. The authors' exposition is clear with a proper amount of detail. this monograph is highly recommended. - Bruce C. Berndt, MathSciNet, American Mathematical Society, Mathematical Reviews on the We very readable bookmaterial ideal as a spur to undergraduate research, and no less as a gateway to the general study of two venerable subjects not often taught to undergraduates anymore: elliptic functions and orthogonal polynomials. --D. V. Feldman, University of New Hampshire, CHOICE, October 2001 The book's strengths lie in its currency, its many worked examples, historical footnotes, and references to the literature. -D.V. Feldman, University of New Hampshire, in CHOICE, April 1998 Author InformationLomont, J.S.; Brillhart, John Tab Content 6Author Website:Countries AvailableAll regions |
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