Cotter — Method of Solving Legendre's and BesseVs Equations. 161 



Bessel's JSquation. — If the equation is written 



{c^IPy + (cBy - ivy) + s^y = 0, 



the first three terms (enclosed in brackets) can be integrated in precisely the 

 same fashion as has been used for Legendre's equation. The form of the 

 solution obtained is either 



or 3/ = { 1 + «- "i?-ia;2« - 1/)- 1^- (« - 1) } - 1 (^^- « + ^^«), 



It is obvious that many other differential equations could be treated in a 

 similar manner. 



It should be pointed out that the series obtained by this method requires 

 to be examined for convergency. The method furnishes no test of 

 the convergency of the series which is arrived at as the solution of 

 equations. 



I 



