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Lectures on the Theory of Elliptic Functions by Harris Hancock ISBN: 0486438252 Dover Publications Price: $75.00 click here to see this book Prized for its extensive coverage of classical material, this text is also well regarded for its unusual fullness of treatment and its comprehensive discussion of both theory and applications. The author developes the theory of elliptic integrals, beginning with formulas establishing the existence, formation, and treatment of all three types, and concluding with the most general description of these integrals in terms of the Riemann surface. The theories of Legendre, Abel, Jacobi, and Weierstrass are developed individually and correlated with the universal laws of Riemann. The important contributory theorems of Hermite and Liouville are also fully developed. 1910 ed. Table of Contents for Lectures on the Theory of Elliptic Functions I. Preliminary Notions II. Function Which Have Algebraic Addition-Theorems III. The Existence of Periodic Functions in General IV. Doubly Periodic Functions. Their Existence. The Periods V. Construction of Doubly Periodic Functions VI. The Reimann Surface VII. The Problem of Inversion VIII. Elliptic Integrals in General IX. The Moduli of Periodicity for the Normal Forms of Legendre and of Weierstrass X. The Jacobi Theta-Functions XI. The Functions sn u, cn u, dn u XII. Doubly Periodic Functions of the Second Sort XIII. Elliptic Integrals of the Second Kind XIV. Introduction ot Weierstrass’s Theory XV. The Weierstrassian Functions XVI. The Addition Theorems XVII. The Sigma-Functions XVIII. The Theta- and Sigma-Functions When Special Values Are Given to the Argument XIX. Elliptic Integrals of the Third Kind XX. Methods of Representing Analytic Doubly Periodic Functions of Any Order Which Have Everywhere in the Finite Portion of the Plane the Character of Integral or (Fractional) Rational Functions XXI. The Determination of All Analytic Functions Which Have Algebraic Addition-Theorems

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