Lectures on the Theory of Elliptic Functions by Harris Hancock - PDF

Book 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 sn?u, cn?u, dn?u 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 P, ?, s 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

About this book :-
"Lectures on the Theory of Elliptic Functions" by "Harris Hancock" is a classic text in "elliptic functions" and "complex analysis". The book systematically introduces the theory of "doubly periodic functions", exploring their algebraic and analytic properties, transformations, and applications. Hancock presents the material in a clear, lecture-style format, making advanced topics accessible to both students and researchers. The book covers fundamental concepts such as the "Weierstrass P-function", Jacobi elliptic functions, addition theorems, and inversion problems. Hancock provides rigorous proofs, examples, and exercises, illustrating the connections between different formulations of elliptic functions and their role in "mathematical analysis". The text also explores practical applications, bridging classical theory with modern approaches in analysis and function theory. Renowned for its clarity, depth, and logical structure, Hancock’s work remains a key reference in "function theory" and the study of complex functions. Its systematic treatment of elliptic functions has influenced generations of mathematicians, physicists, and engineers. This book is essential for anyone seeking a solid foundation in the theory, properties, and applications of "complex functions" in advanced mathematics.

Book Detail :-
Title: Lectures on the Theory of Elliptic Functions by Harris Hancock - PDF
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 Author :-
The author Harris Hancock (1823–1903) was an American mathematician known for his work on "elliptic functions", "complex analysis", and "function theory". He taught at Harvard University and the United States Naval Academy, emphasizing clarity, rigor, and systematic presentation in mathematics. Hancock authored influential texts, including "Lectures on the Theory of Elliptic Functions", which remains a foundational reference in "mathematical analysis" and "complex functions". His books combined clear explanations with rigorous proofs, inspiring generations of mathematicians, students, and engineers, and bridging classical theory with modern approaches in advanced mathematics.

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