ON SOME EELATIONS BETWEEN BESSEL FUNC- 

 TIONS OF THE FIRST AND OF THE SECOND 

 KIND.* 



Alexander S. Chessin. 

 The'general solution of Bessel's equation 



^^^ l^ + ^^+(l--^)^ = ^ 



is of the form 



(2) y = AJAx) + BK„(x), 



or of the form 



(2)' y = AJ„ (x)-\-BJ_„(x), 



according as n is, or is not, an integral number, A and B 

 being arbitrary constants, while «/„ (x) and ir„ (x) denote 

 Bessel functions of the first and of the second kind, the func- 

 tions Jnijx) and J_^ (x) being distinct and independent when 

 n is not an integral number. 



The differential equation ( 1 ) may be presented in a different 

 form, namely 



^^y ^^^+(^-^V^^=°- 



or, we may say that u =:y\/x is the general solution of the 

 differential equation 



(jPu 



* Presented by title to The Academy of Science of St. Louis, October 

 20, 1902. 



(99) 



