V.—The Periodic Lamé Functions

Abstract

Any solution of the Lamé equationin which sn u has the modulus k, may be termed a Lamé function, but this paper is devoted mainly to functions of real periods 2K or 4K. We suppose that k2 ≤ 1; the number n is real, but not necessarily an integer, and it is sufficient to take n ≥ − ½. These periodic solutions exist for certain characteristic values of h; a table of such values is included in this paper.