An Elementary Treatise on Elliptic Functions by Arthur Cayley
An Elementary Treatise on Elliptic Function - Table of Contents
- 1. General Outline
- 2. The Addition-Equation. Landen’s Theorem
- 3. Miscellaneous Investigations
- 4. On the Elliptic Functions sn, cn, dn
- 5. The Three Kinds of Elliptic Integrals
- 6. The Functions T(u), H(u), Z(u), T2(u), T3(u), T4(u)
- 7. Transformation. General Outline
- 8. The Quadratic Transformation (n = 2); and the Odd-Prime Transformations (n = 3, 5, 7). Properties of the Modular Equation and the Multiplier
- 9. Jacobi’s Partial Differential Equations for H, T, and for the Numerators and Denominators in the Multiplication and Transformation of the Elliptic Functions sn, cn, dn
- 10. Transformation for an Odd n, and in Particular an Odd-Prime Order: Development of the Theory by Means of the Expansion of the Complete Functions
- 11. The q-Functions: Further Theory of the Functions H, T
- 12. Reduction of a Differential Expression
- 13. Quadratic Transformation of the Elliptic Integrals of the First and Second Kinds: The Arithmetic–Geometric Mean
- 14. The General Differential Equation
- 15. On the Determination of Certain Curves whose Arc is Represented by an Elliptic Integral of the First Kind
- 16. On Two Integrals Reducible to Elliptic Integrals
What You Will Learn in An Elementary Treatise on Elliptic Function
An Elementary Treatise on Elliptic Functions by Arthur Cayley is a historic mathematical reference designed to establish a solid foundation in classical complex analysis and special functions. Developed as an authoritative university text, this comprehensive elliptic functions textbook for university students focuses on Jacobi's elliptic functions (sn, cn, dn), Landen's transformation, and the geometric applications of elliptic integrals.
Cayley’s approach is direct, algebraic, and computational. Each theorem is developed with detailed step-by-step derivations, allowing readers to learn elliptic functions concepts step-by-step—from basic addition formulas and period lattices to theta functions and modular equations. This clear methodology makes the volume an essential elementary treatise on elliptic functions pdf resource for understanding higher-level analysis.
Ideal for mathematics major students, theoretical physicists, and research historians, this landmark volume serves as a powerful free special functions textbook for advanced students. Available as an open-access study guide, it remains a reliable elliptic functions study guide for self-learners aiming to master the foundational formulas powering classical mechanics and number theory.
Book Details & Specifications
Title:
An Elementary Treatise on Elliptic Functions by Arthur Cayley
Publisher:
G. Bell and sons
Year:
1895
Pages:
411
Type:
PDF
Language:
English
ISBN-10 #:
1429700491
ISBN-13 #:
978-1429700498
License:
Public Domain Work
Amazon:
Amazon
About the Author: Arthur Cayley
The author Arthur Cayley
(1821–1895) was a legendary British mathematician, Sadlerian Professor of Pure Mathematics at Cambridge University, and one of the most prolific founders of modern pure mathematics, pioneer of matrix algebra, group theory, and invariant theory.
His classic work An Elementary Treatise on Elliptic Functions PDF by Arthur Cayley stands as a landmark masterwork of 19th-century mathematical exposition and special function theory.
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