Lamé functions of the first kind generated by computer

The definitions of the Lamé functions and the ellipsoidal coordinates inherent to them are introduced. Proceeding from Lamé's differential equation the four classes of Lamé functions of the first kind are generated by computer with the aid of formula manipulation techniques. For this purpose algebraic expressions for the coefficients in the Lamé polynomials are constructed by virtue of recurrence formulae and presented in tabular as well as machine readable form for further processing. The determination of a parameter appearing in the polynomial coefficients leads to an algebraic eigenvalue problem. It is shown how this eigenvalue problem is amenable to numerical treatment. The polynomial coefficients together with the eigenvalues are characteristic for the Lamé functions and define them completely.