Theory of Elliptic Integrals by Harris Hancock
Theory of Elliptic Integrals - Table of Contents
- 0. Introduction
- 1. Elliptic Integrals of the First, Second and Third Kinds.
- 2. The Legendre Transformations
- 3. The Elliptic Functions
- 4. Elliptic Integrals of the First Kind Reduced to Legendre's Normal Form
- 5. Numerical Computation of the Elliptic Integrals of the First and Second Kinds.
- 6. Landen's Transformation
- 7. Miscellaneous Examples and Problems
- 8. Five Place Tables
What You Will Learn in Theory of Elliptic Integrals
Elliptic Integrals by Harris Hancock is a foundational, classic work that offers a rigorous, comprehensive treatment of non-elementary integrals and special functions. Designed for advanced mathematics students and researchers, this timeless volume systematically demystifies Legendre transformations and Jacobian elliptic forms, making it an indispensable reference for advanced elliptic integrals study practice.
The monograph delves deeply into the three standard kinds of elliptic integrals, Landen’s transformations, and the reduction of general algebraic integrals. By pairing rigorous theoretical developments with clear computational procedures, Hancock enables readers to approach step-by-step special functions integration rules with high analytical precision and mathematical clarity.
Widely respected by historians of mathematics and university researchers, this volume remains an essential companion for courses in classical analysis and applied physics. Hancock’s structured approach equips mathematicians with the foundational analytical skills required for mastering classic elliptic functions evaluation techniques across complex analysis.
Book Details & Specifications
Title:
Theory of Elliptic Integrals by Harris Hancock
Publisher:
J. Wiley
Year:
1917
Pages:
118
Type:
PDF
Language:
English
ISBN-10 #:
0486604845
ISBN-13 #:
978-0486604848
License:
Public Domain Work
Amazon:
Amazon
About the Author: Harris Hancock
The author Harris Hancock
(1867–1944) was a prominent American mathematician and long-serving professor of mathematics at the University of Cincinnati. He studied under legendary European mathematicians, including Weierstrass and Fuchs, gaining deep insights into advanced analysis.
Author of several influential treatises on algebraic numbers, calculus of variations, and special functions, Hancock contributed significantly to American mathematical pedagogy. His monumental classical texts remain highly valued references for modern scholars seeking foundational classical mathematics analysis resources.
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