{"product_id":"elliptic-polynomials-by-j-s-lomont-john-brillhart-scholarly","title":"Elliptic Polynomials by J.S. Lomont \u0026 John Brillhart - Scholarly","description":"\u003cp\u003eIn this review of Elliptic Polynomials, the authors J.S. Lomont and John Brillhart present a focused monograph aimed at researchers and advanced students who want a bridge between \u003cstrong\u003eelliptic functions\u003c\/strong\u003e and orthogonal polynomials. The bottom line: this is a specialized, rigorous treatment best suited for mathematicians interested in the structural links and explicit constructions that arise when odd Jacobi elliptic functions generate polynomial families. The book's chief draw is the novel development of weight functions, measures and identities that arise from elliptic integrals.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eInterdisciplinary focus:\u003c\/strong\u003e Explores the interplay between \u003cstrong\u003eelliptic functions\u003c\/strong\u003e and orthogonal polynomials, giving readers a coherent narrative linking the two areas.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eNew material:\u003c\/strong\u003e Presents original results about classes of polynomials generated by odd elliptic integrals, useful for further theoretical work.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eOrthogonality construction:\u003c\/strong\u003e Develops weight functions and measures explicitly, helping readers apply these polynomials in analytic contexts.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eTechnical evaluations:\u003c\/strong\u003e Provides structure constants and inequalities that support rigorous estimates and further derivations.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFunction inverses:\u003c\/strong\u003e Covers odd Jacobi elliptic functions and their inverses, clarifying inversion relations used in constructing polynomial families.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eElliptic Polynomials is primarily for professional mathematicians, graduate students in pure mathematics, and researchers in special functions who already have familiarity with elliptic functions or orthogonal polynomial theory. The treatment assumes comfort with advanced analysis and classical function theory rather than introductory exposition.\u003c\/p\u003e\n\u003cp\u003eReaders seeking a textbook-style introduction or applied numerical algorithms should look elsewhere, since this monograph emphasizes structural results, explicit formulas, and theoretical connections over pedagogical progression or computational recipes.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eClear presentation of the link between \u003cstrong\u003eelliptic integrals\u003c\/strong\u003e and polynomial generation, valuable for theoretical development.\u003c\/li\u003e\n\u003cli\u003eConcrete construction of weight functions and measures that illuminate orthogonality properties.\u003c\/li\u003e\n\u003cli\u003eNew inequalities and structure constants that make subsequent work and comparisons easier.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe material is specialized and assumes significant background, so it is not suited to beginners seeking an introduction.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eElliptic Polynomials\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eJ.S. Lomont, John Brillhart\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject\u003c\/td\u003e\n\u003ctd\u003eElliptic functions and orthogonal polynomials\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eCoverage\u003c\/td\u003e\n\u003ctd\u003eOdd Jacobi elliptic functions, inverses, weight functions\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIncludes\u003c\/td\u003e\n\u003ctd\u003eStructure constants, inequalities, explicit formulas\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAudience\u003c\/td\u003e\n\u003ctd\u003eResearchers and advanced graduate students in mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eElliptic Polynomials is a valuable, tightly focused monograph for those working at the intersection of special functions and orthogonal polynomials; its explicit constructions and inequalities make it good value for researchers who will use the formulas and measures in further theoretical work.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book introduce elliptic functions from scratch?\u003c\/strong\u003e\u003cbr\u003eAnswer. No, the text assumes prior familiarity with elliptic functions and moves quickly into connections with polynomial constructions.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eAre computational algorithms provided?\u003c\/strong\u003e\u003cbr\u003eAnswer. The emphasis is theoretical: explicit formulas and evaluations appear, but practical numerical algorithms are not the focus.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWho benefits most from reading this book?\u003c\/strong\u003e\u003cbr\u003eAnswer. Researchers in pure mathematics and advanced graduate students studying special functions or orthogonal polynomials will benefit most.\u003c\/p\u003e","brand":"J.S. 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