Elliptic Polynomials

ISBN-13: 9780367398200 / Angielski / Miękka / 2019 / 320 str.

J. S. Lomont; John Brillhart

Opis

A 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 of the basic aspects of each. Although some of the material may be familiar, it establishes a new mathematical field that intersects with classical subjects at many points. The wealth of information on important properties of polynomials and a clear, accessible presentation make this book valuable to those in real and complex analysis, number theory, and combinatorics, and it will undoubtedly generate further research.

Spis treści

Introduction; 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 Questions

O autorze

Lomont, J.S.; Brillhart, John