DIFFERENTIAL EQUATIONS 



9.032 



2-4-6 . . . . 2H 



P'2n+l(o) = O, 



(-I)P B (S). 



9.033 If 2 = r cos 6: 



dP n (cos 0) n+ i 

 dz r 



9.034 Rodrigues' Formula: 



9.035 If z = r cos 0: 



9.036 If w ^ n : 



0)Pn(cOS0) -P n +l(cOS0)| 



where: 



k = o 



1-3-5 O- i) 



r! 



MEHLER'S INTEGRALS 



9.040 For all values of n: 



2 fd cos (n + I) 

 P n (cos0) = - / c V Qs ^ 2 _ 



9.041 If n is a positive integer: 



COS0) 



LAPLACE'S INTEGRALS, FOR ALL VALUES OF n 



9.042 



9.043 



x /v 



P w (x) = - I [ 



^^o 



/oo 

 T- 

 {o; 



- i cos 



d(t> 



