Elliptic polynomials

Includes index

Includes bibliography (p. 271-276) and references

1: Binomial Sequences of Polynomials (a) The functions F (b) The functions Fo- The sequences {Gm(z)} and {Hm(z)} 2: The Binomial Sequences Generated from f-1, f ∈Fo 3: The Functions F1 - Elliptic Polynomials of the First Kind 4: The Moment Polynomials- Pn(x,y), Qn(x,y), and Rn(x,y) 5: The Functions F1-1 - Elliptic Polynomials of Second Kind 6: Inner Products, Integrals, and Moments- Favard's Theorem 7: The Functions F2- Orthogonal Sequences {Gm(z)}, {Hm(z)} 8: The Functions in Classes I and II (a) Class I Functions- The elliptic functions sn (t, k) (b) Class II Functions- The polynomials f*(t, k) 9: The Tangent Numbers 10: Class III Functions- The n(x) Polynomials 11: Coefficients of the n(x) Polynomials 12: The ⋋n(x) Polynomials 13: The Orthogonal Sequences {Am(z)} and {Bm(z)} 14: The Weight Functions for {Am(z)} and {Bm(z)} 15: Miscellaneous Results 16: Uniqueness and Completion Results 17: Polynomial Inequalities 18: Some Concluding Questio

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.