Tables of Lamé Polynomials

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.