Abstract
There are five different forms used for the Lamé's equation itself, the Jacobian, the Weierstrassian, two algebraic forms and one trigonometric. Modern literature uses the Jacobian form as a basis. Lamé's equation has one even and one odd solution. This chapter discusses Stieltjes' theorem on the zeros of Lamé polynomials. It focuses on the eight types of Lamé polynomial. Products of two (identical) Lamé polynomials are very important; they are sometimes known as ellipsoidal harmonics.
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