256 USEFUL FORMULAE, CONNECTING LEGENDRE'S COEFFICIENTS, WHICH 

 which is a very elegant formula for finding 



(I-/* 2 

 but when m = 0, 



Making the same substitution in equation (7'), we have 



t 



1.2.8... (n-m) 



_ 1.3.5 ... (2n-5) , 4 _, , .1.3.5 ... (2n-3) 



= T727TT^rr2< -^ ) r2.3...i^^^- 1 



or -u 



M ' 



which is a convenient formula. 



In order to complete the determination of the quantities H, &c. we must 

 remember that, when m is greater than n, the quantity H vanishes ; when 

 m = n we have 



fl:-(i-y) : , 



and when n m+l, we have 



Also 

 and 



is. Let G:(I - 



Then from equation (9) we get 



