E-Book, Englisch, 560 Seiten, Web PDF
Arscott / Khabaza Tables of Lamé Polynomials
1. Auflage 2014
ISBN: 978-1-4831-8471-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Mathematical Tables
E-Book, Englisch, 560 Seiten, Web PDF
ISBN: 978-1-4831-8471-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Tables of Lamé polynomials presents tables of Lamé polynomials, which were calculated on the Ferranti 'Mercury' machine at the London University Computer Unit in England. Lamé polynomials are solutions of Lamé differential equation, which is used in a number of different forms, including the 'Jacobian form'. A particular Lamé polynomial is specified completely (apart from a constant multiplier) by the type number, the value of N, and the position of the corresponding eigenvalue of h in the set of such eigenvalues. Comprised of three chapters, this volume begins with an introduction to the theory of Lamé polynomials and the equations involved, together with their elementary properties and correspondence with other notations. The tabulated form of Lamé polynomials and the method of tabulation are discussed, and approximations in limiting cases are considered. The next chapter deals with the method of computation of the Lamé polynomials, including the calculation of the coefficients, eigenroots, and eigenvectors. The book concludes with a description of the instructions and terms used in the program using the PIG input routine on the Ferranti 'Mercury' computer. This monograph will be of interest to mathematicians and mathematics students.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Tables of Lamé Polynomials;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;CHAPTER 1. SUMMARY OF THE THEORY OF LAMÉ POLYNOMIALS;10
6.1;1.1 LAMÉ'S EQUATION;10
6.2;1.2 LAMÉ POLYNOMIALS;11
6.3;1.3 ELEMENTARY PROPERTIES;12
6.4;1.4 CORRESPONDENC WITH OTHER NOTATIONS;12
6.5;1.5 TABULATED FORM OF THE POLYNOMIALS;12
6.6;1.6 METHOD OF TABULATION;13
6.7;1.7 RELATION BETWEEN EIGENVALUES FOR k2 AND k'2;14
6.8;1.8 APPROXIMATIONS IN LIMITING CASES;15
7;CHAPTER 2. THE METHOD OF COMPUTATION;19
7.1;2.1 STATEMENT OF THE PROBLEM;19
7.2;2.2 CALCULATION OF THE COEFFICIENTS;19
7.3;2.3 CALCULATION OF THE EIGENROOTS;19
7.4;2.4 CALCULATION OF THE EIGENVECTORS;20
7.5;2.5 A SCHEMATIC VERSION OF THE PROGRAMME;21
8;CHAPTER 3. THE FERRANTI PROGRAMME;23
8.1;3.1 INSTRUCTION CODE;23
8.2;3.2 SPECIFICATIONS;24
8.3;3.3 CALCULATION OF THE COEFFICIENTS;24
8.4;3.4 CALCULATION OF THE EIGENROOTS;25
8.5;3.5 CALCULATION OF THE EIGENVECTOR;25
