Elliptic Polynomials

ISBN-13: 9781584882107 / Angielski / Twarda / 2000 / 320 str.

J. S. Lomont; John Brillhart; John S. Lomont

Opis

The term elliptic polynomials refers to the polynomials generated by o dd elliptic integrals and elliptic functions. In studying these, the a uthors consider such things as orthogonality and the construction of w eight functions and measures, finding structure constants and interest ing inequalities, and deriving useful formulas and evaluations. Althou gh some of the material may be familiar, it establishes a new mathemat ical field that intersects with classical subjects at many points. Its wealth of information on important properties of polynomials and clea r, accessible presentation make Elliptic Polynomials valuable to those in real and complex analysis, number theory, and combinatorics, and w ill 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