DIFFERENTIAL EQUATIONS 219 



Airey, 1. c. First 10 roots, 5 decimal places. 

 Roots of- 



n _ 



" 



/(*) 



Airey, 1. c. First 10 roots: n = o, 4 decimal places, n = i, 2, 3, 3 decimal 

 places. 



Jahnke and Emde, Table XXV, first 5 roots for n = o, 3 for n = i, 2 for 

 n = 2: 4 figures. 



Airey, 1. c. gives roots of some other equations involving Bessel's functions 

 connected with the vibration of circular plates. 



Roots of: 



J v (x)Y v (x) = J v (kx)Y v (kx). 



Jahnke and Emde, Table XXVI, first 6 roots, 4 decimal places, for 



V = O, 1/2, I, 3/2, 2, 5/2: & = 1.2, 1.5, 2.0. 



Table XXVIII, first root, multiplied by ( - i) f or k = i, 1.2, 1.5, 2-11, 

 19, 39, oo: v same as above. 



Table XXIX, first 4 roots, multiplied by (k - i) for certain irrational values 

 of kj and v = o, i. 



