Lectures on the Theory of Elliptic Functions Book

Chapter I	Preliminary Notions
	Rational Functions
	Principal Analytical Forms of Rational Functions
	Trigonometric Functions
	Infinite Products
	The General Trigonometric Functions
	Analytic Functions
Chapter II	Functions which have Algebraic Addition-Theorems
	The Discussion Restricted to One-valued Functions
	Continuation of the Domain in which the Analytic Function [phi](u) has been Defined, with Proofs that its Characteristic Properties are Retained in the Extended Domain
Chapter III	The Existence of Periodic Functions in General
	The Period-Strips
	The Eliminant Equation
Chapter IV	Doubly Periodic Functions. Their Existence. The Periods
Chapter V	Construction of Doubly Periodic Functions
	The General Doubly Periodic Function Expressed through a Simple Transcendent
	The Eliminant Equation
Chapter VI	The Riemann Surface
	The One-valued Functions of Position on the Riemann Surface
	The Zeros of the One-valued Functions of Position
	Integration
	Realms of Rationality
Chapter VII	The Problem of Inversion
Chapter VIII	Elliptic Integrals in General
	Legendre's Normal Forms
Chapter IX	The Moduli of Periodicity for the Normal forms of Legendre and of Weierstrass
Chapter X	The Jacobi Theta-Functions
	Expression of the Theta-Functions in the Form of Infinite Products
	The Small Theta-Functions
Chapter XI	The Functions sn u, cn u, dn u
	Development of the Elliptic Functions in Simple Series of Sines and Cosines
Chapter XII	Doubly Periodic Functions of the Second Sort
Chapter XIII	Elliptic Integrals of the Second Kind
Chapter XIV	Introduction to Weierstrass's Theory
Chapter XV	The Weierstrassian Functions [characters not reproducible]u, [xi]u, [sigma]u
	The Sigma-Function
	The [xi]u-Function
Chapter XVI	The Addition-Theorems
	Addition-Theorems for the Weierstrassian Functions
Chapter XVII	The Sigma-Functions
	Differential Equations which are satisfied by Sigma-Quotients
	Addition-Theorems for the Sigma-Functions
	Expansion of the Sigma-Functions in Powers of the Argument
Chapter XVIII	The Theta- and Sigma-Functions When Special Values are Given to the Argument
Chapter XIX	Elliptic Integrals of the Third Kind
	The Omega-Function
	Addition-Theorems for the Integrals of the Third Kind
Chapter XX	Methods of Representing Analytically Doubly Periodic Functions of any Order Which have Everywhere in the Finite Portion of the Plane the Character of Integral of (Fractional) Rational Functions
Chapter XXI	The Determination of all Analytic Functions Which have Algebraic Addition-Theorems
	Table of Formulas