Elliptic Polynomials

by J.S. Lomont, John Brillhart

Overview

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 basic aspects of each. It presents new material about various classes of polynomials and about t

Product Details

ISBN-13:	9781040218365
Publisher:	CRC Press
Publication date:	08/31/2000
Sold by:	Barnes & Noble
Format:	eBook
Pages:	320
File size:	1 MB

About the Author

Lomont, J.S.; Brillhart, John

Table of Contents

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 -1, where 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

Editorial Reviews

This book explores the interplay between the fields of elliptic functions and orthogonal polynomials, considering such topics as orthogonality and the construction of weight functions and measures, finding structure constants, and deriving useful formulas and evaluations. It also provides new material about Jacobi elliptic functions through the use of Maclaurin series divisibility, and introduces a new class of polynomials, "moment polynomials", which give the moments of orthogonal sequences. Lomont and Brillhart (both U. of Arizona, Tucson) have written this text for people involved in real and complex analysis, number theory and combinatorics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews