where is the Ferrers function of the first kind (§14.3(i)), , and the coefficients are given by
Then the set of coefficients , is the solution of the difference equation
(note that ) that satisfies the normalizing condition
Also, as ,
where and are again the Ferrers functions and . The coefficients satisfy (30.8.4) for all when we set for . For they agree with the coefficients defined in §30.8(i). For they are determined from (30.8.4) by forward recursion using . The set of coefficients , , is the recessive solution of (30.8.4) as that is normalized by
It should be noted that if the forward recursion (30.8.4) beginning with , leads to , then is undefined for and does not exist.