Laplace, Lamé, and Bessel's Functions by Isaac Todhunter
Laplace, Lamé, and Bessel's Functions - Table of Contents
- 1. General Introduction & Historical Overview
- 2. Other Forms of Legendre’s Coefficients
- 3. Fundamental Properties of Legendre’s Coefficients
- 4. Coefficients Expressed by Definite Integrals
- 5. Differential Equations of Legendre Coefficients
- 6. Legendre Coefficients of the Second Kind
- 7. Asymptotic Values of High-Order Coefficients
- 8. Properties of Associated Legendre Functions
- 9. Expansions Using Continued Fractions
- 10. Numerical Methods & Approximate Quadrature
- 11. Expansion of Functions in Legendre Series
- 12. Miscellaneous Analytical Propositions (Part I)
- 13. Introduction to Laplace’s Coefficients
- 14. Advanced Investigations of Laplace’s Coefficients
- 15. General Theory of Laplace’s Functions
- 16. Expansion of Arbitrary Functions
- 17. Alternative Proofs for Function Expansions
- 18. Trigonometrical Series in Sines and Cosines
- 19. Rigorous Analysis of Dirichlet’s Investigation
- 20. Miscellaneous Analytical Theorems
- 21. Systems of Special Curvilinear Coordinates
- 22. Analysis of General Curvilinear Coordinates
- 23. Transformation of Laplace’s Principal Equation
- 24. Transformation of Laplace’s Secondary Equation
- 25. Physical Applications in Potential Theory
- 26. Introduction to Lamé’s Functions
- 27. Ellipsoidal Harmonics & Separation of Terms
- 28. Special Cases of Lamé’s Functions
- 29. Miscellaneous Propositions on Lamé Functions
- 30. Mathematical Definition of Bessel’s Functions
- 31. Fundamental Properties of Bessel’s Functions
- 32. Fourier’s Integral Expression for Bessel Functions
- 33. Analysis of Large Roots of Fourier’s Equation
- 34. Expansions in Series of Bessel Functions
- 35. General Theorems on Orthogonal Expansions
- 36. Miscellaneous Propositions (Part II)
What You Will Learn in Laplace, Lamé, and Bessel's Functions
An Elementary Treatise on Laplace's Functions, Lamé's Functions, and Bessel's Functions by Isaac Todhunter is an authoritative historical text written for students of mathematical physics and applied analysis. Serving as an essential special functions textbook for graduate students, this classic work connects differential equations with physical potential theory.
Todhunter’s rigorous pedagogical structure enables readers to learn laplace and bessel functions step-by-step. Topics transition systematically from Legendre polynomials and spherical harmonics to Lamé’s ellipsoidal functions and Bessel’s cylindrical coefficients, making this a complete isaac todhunter laplace functions pdf study guide.
Ideal for university scholars, mathematical historians, and theoretical physicists, this historic text offers a valuable free mathematical physics textbook for beginners. Available as an accessible public domain open-access monograph, it stands as an indispensable spherical harmonics study guide for self-learners mastering partial differential equations.
Book Details & Specifications
Title:
Laplace, Lamé, and Bessel's Functions by Isaac Todhunter
Publisher:
Macmillan
Year:
1875
Pages:
368
Type:
PDF
Language:
English
ISBN-10 #:
0469127104
ISBN-13 #:
978-0469127104
License:
Public Domain Work
Amazon:
Amazon
About the Author: Isaac Todhunter
The author Isaac Todhunter
(1820–1884) was a world-renowned English mathematician, Fellow of St John's College, Cambridge, and Fellow of the Royal Society, celebrated globally for writing standard textbook treatises that shaped 19th-century British mathematics education.
His masterwork, Laplace's, Lamé's, and Bessel's Functions PDF by Isaac Todhunter, remains one of the most historically significant treatises on special functions in physical dynamics.
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