252 



REPORTS ON THE STATE OF SCIENCE, ETC. 



Zeros of Bessel Functions oi small fractional order. 



The first zero, pi of Jv (x), was calculated from the relation 



2- 10 7v+19 

 P* = 2 9 (v+l) 5 (v+2) 2 (v + 3)(v+4)(v+5) [ 



When v is small, approximate values of p* and p 3 are sufficient to give the value of 

 p, to five places of decimals. If v = — 1+a and a is less than 0-15, then to five 

 places of decimals, 



^^(i+j-^+Ar- ) 



A short table* of the zeros to four places for the range v= — J to 1 was published 

 some years ago. 



* J. R. Airey. " Bessel functions of small fractional order and their application 

 to problems of Elastic Stability." Phil. Mag., vol. 41, 1921, pp. 200-205. 



Zero p, of the Bessel Function, J„ (x). 



