IQ2 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



9.02 Recurrence formulae for P n (x): 



i. (n + i)Pn+i + nPn-i = (2n + i)xP r 



( 2w+I )P n = ^-^. 



3 . 



dP 



n n 



4. nP n = x -- j 



dx dx 



5- (i-* 2 )^=(n+ 



6. (i - x*) ^ = n(P^ - xP n ). 



7- (2 + I) (I - * 2 ) ^ = ( + I) (Pn-l ~ P n+ l). 



9.028 Recurrence formulae for Q n (x). These are the same as those for P n (x). 



9.030 Special Values. 



PoM = i, 



PlO) = X, 



- 5), 



- 35^), 



6930^ - 1260^ + 35) 



9.031 



. X I , X+ I 





- i, 



-I 2 



