Lectures on the Theory of Elliptic Functions by Harris Hancock
Theory of Elliptic Functions - Table of Contents
- 1. Preliminary Notions – Rational Functions, Principal Analytical Forms of Rational Functions, Trigonometric Functions, Infinite Products, The General Trigonometric Functions, Analytic Functions
- 2. Functions Which Have Algebraic Addition-Theorems
- 3. The Existence of Periodic Functions in General
- 4. Doubly Periodic Functions: Their Existence and the Periods
- 5. Construction of Doubly Periodic Functions
- 6. The Riemann Surface
- 7. The Problem of Inversion
- 8. Elliptic Integrals in General
- 9. The Moduli of Periodicity for the Normal Forms of Legendre and of Weierstrass
- 10. The Jacobi Theta-Functions
- 11. The Functions
- 12. Doubly Periodic Functions of the Second Sort
- 13. Elliptic Integrals of the Second Kind
- 14. Introduction to Weierstrass's Theory
- 15. The Weierstrassian Functions
- 16. The Addition Theorems
- 17. The Sigma-Functions
- 18. The Theta- and Sigma-Functions When Special Values Are Given to the Argument
- 19. Elliptic Integrals of the Third Kind
- 20. Methods of Representing Analytically Doubly Periodic Functions of Any Order Which Have Everywhere in the Finite Portion of the Plane the Character of Integral or (Fractional) Rational Functions
- 21. The Determination of All Analytic Functions Which Have Algebraic Addition-Theorems
What You Will Learn in Theory of Elliptic Functions
Theory of Elliptic Functions by Harris Hancock is a landmark classical treatise that provides an in-depth, rigorous exploration of complex functions, Riemann surfaces, and periodic systems. Designed for advanced graduate students and research mathematicians, this foundational work bridges elementary calculus and higher complex analysis, making it an indispensable resource for advanced elliptic function theory practice.
The volume systematically covers doubly periodic functions, Weierstrassian p-functions, Jacobi theta-functions, and algebraic addition theorems. By combining detailed analytical derivations with scaffolded geometric representations, Hancock enables readers to understand complex transformations and apply step-by-step doubly periodic functions rules with absolute analytical precision.
Widely celebrated by historians of mathematics and university researchers, this comprehensive text remains an authoritative guide for advanced courses in complex analysis. Hancock's structured framework equips scholars with the classical analytical tools required for mastering higher complex variable transformation methods across pure and applied mathematics.
Book Details & Specifications
Title:
Lectures on the Theory of Elliptic Functions by Harris Hancock
Publisher:
J. Wiley & sons
Year:
1910
Pages:
536
Type:
PDF
Language:
English
ISBN-10 #:
054864344X
ISBN-13 #:
978-0548643440
License:
Public Domain Work
Amazon:
Amazon
About the Author: Harris Hancock
The author Harris Hancock
(1867–1944) was a distinguished American mathematician and Professor of Mathematics at the University of Cincinnati. Having studied directly under European masters such as Karl Weierstrass, Lazarus Fuchs, and Leopold Kronecker, he brought elite European analytic traditions to American higher education.
As the author of foundational monographs on algebraic numbers, calculus of variations, and special functions, Hancock played a vital role in establishing rigorous graduate mathematics. His classical works continue to be revered globally as essential university level complex analysis resources and scholarly reference guides.
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