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• catalog abstract ""An 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 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."--Jacket.".
• catalog contributor b12259795.
• catalog contributor b12259796.
• catalog created "c2001.".
• catalog date "2001".
• catalog date "c2001.".
• catalog dateCopyrighted "c2001.".
• catalog description ""Although some of the material may be familiar, it establishes a new mathematical field that intersects 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."--Jacket.".
• catalog description ""An 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."".
• catalog description "Binomial Sequences of Polynomials -- The functions F -- The functions F[subscript 0]--The sequences {G[subscript m](z)} and {H[subscript m](z)} -- The Binomial Sequences Generated from f[superscript -1], f [set membership] F[superscript 0] -- The Functions F[subscript 1]--Elliptic Polynomials of the First Kind -- The Moment Polynomials--P[subscript n](x, y), Q[subscript n](x, y), and R[subscript n](x, y) -- The Functions F[superscript -1 subscript 1]--Elliptic Polynomials of Second Kind -- Inner Products, Integrals, and Moments--Favard's Theorem -- The Functions F[subscript 2]--Orthogonal Sequences {G[subscript m](z)}, {H[subscript m](z)} -- The Functions in Classes I and II -- Class I Functions--The elliptic functions sn (t, k) -- Class II Functions--The polynomials f*(t, k) -- The Tangent Numbers -- Class III Functions--The [delta subscript n](x) Polynomials -- Coefficients of the [delta subscript n](x) Polynomials -- The [lambda subscript n](x) Polynomials -- The Orthogonal Sequences {A[subscript m](z)} and {B[subscript m](z)} -- The Weight Functions for {A[subscript m](z)} and {B[subscript m](z)} -- Miscellaneous Results -- Uniqueness and Completion Results -- Polynomial Inequalities.".
• catalog description "Includes bibliographical references (p. [271]-276) and indexes.".
• catalog extent "xxiii, 289 p. ;".
• catalog identifier "1584882107 (alk. paper)".
• catalog issued "2001".
• catalog issued "c2001.".
• catalog language "eng".
• catalog publisher "Boca Raton : Chapman & Hall/CRC,".
• catalog subject "515/.983 21".
• catalog subject "Elliptic functions.".
• catalog subject "Polynomials.".
• catalog subject "QA343 .L68 2001".
• catalog tableOfContents "Binomial Sequences of Polynomials -- The functions F -- The functions F[subscript 0]--The sequences {G[subscript m](z)} and {H[subscript m](z)} -- The Binomial Sequences Generated from f[superscript -1], f [set membership] F[superscript 0] -- The Functions F[subscript 1]--Elliptic Polynomials of the First Kind -- The Moment Polynomials--P[subscript n](x, y), Q[subscript n](x, y), and R[subscript n](x, y) -- The Functions F[superscript -1 subscript 1]--Elliptic Polynomials of Second Kind -- Inner Products, Integrals, and Moments--Favard's Theorem -- The Functions F[subscript 2]--Orthogonal Sequences {G[subscript m](z)}, {H[subscript m](z)} -- The Functions in Classes I and II -- Class I Functions--The elliptic functions sn (t, k) -- Class II Functions--The polynomials f*(t, k) -- The Tangent Numbers -- Class III Functions--The [delta subscript n](x) Polynomials -- Coefficients of the [delta subscript n](x) Polynomials -- The [lambda subscript n](x) Polynomials -- The Orthogonal Sequences {A[subscript m](z)} and {B[subscript m](z)} -- The Weight Functions for {A[subscript m](z)} and {B[subscript m](z)} -- Miscellaneous Results -- Uniqueness and Completion Results -- Polynomial Inequalities.".
• catalog title "Elliptic polynomials / J.S. Lomont, John Brillhart.".
• catalog type "text".