# §29.17 Other Solutions

## §29.17(i) Second Solution

If (29.2.1) admits a Lamé polynomial solution , then a second linearly independent solution is given by

For properties of these solutions see Arscott (1964b, §9.7), Erdélyi et al. (1955, §15.5.1), Shail (1980), and Sleeman (1966b).

## §29.17(ii) Algebraic Lamé Functions

Algebraic Lamé functions are solutions of (29.2.1) when is half an odd integer. They are algebraic functions of , , and , and have primitive period . See Erdélyi (1941c), Ince (1940b), and Lambe (1952).

## §29.17(iii) Lamé–Wangerin Functions

Lamé–Wangerin functions are solutions of (29.2.1) with the property that is bounded on the line segment from to . See Erdélyi et al. (1955, §15.6).