§29.8 Integral Equations

Let be any solution of (29.2.1) of period , be a linearly independent solution, and denote their Wronskian. Also let be defined by

where are real, and , , are the Jacobian elliptic functions (§22.2). Then

where is the Ferrers function of the first kind (§14.3(i)),

29.8.3

and (= ) and are determined by

A special case of (29.8.2) is

where

Others are:

and

For further integral equations see Arscott (1964a), Erdélyi et al. (1955, §15.5.3), Shail (1980), Sleeman (1968a), and Volkmer (1982, 1983, 1984).