2l8 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



G(x) = - V~ 2 n (-} x-Vi (-} = 1 x-l 



\4/ \2/ 0.78012 



1.15407 



Table I of Jahnke and Emde gives these two functions to 3 decimal places 

 for x = 0.2 to x = 8.0, interval 0.2, and x = 8.0 to x = 12.0, interval i.o. 



Roots of JQ(X) = o. 



Airey, Phil. Mag. 36, p. 241, 1918: First 40 roots (p) with corresponding 

 values of /i(p), 7 decimal places. 



Jahnke and Emde, Table IV, same, to 4 decimal places. 



Roots of Ji(x) = o. 



Gray and Mathews, Table III, first 50 roots, with corresponding values 

 of Jo(x), 1 6 decimal places. 



Airey, Phil. Mag. 36, p. 241: First 40 roots (r) with corresponding values 

 of /o(r), 7 decimal places. 



Jahnke and Emde, Table IV, same, to 4 decimal places. 



Roots of J n (x) = o. 



B. A. Report, 1917, first 10 roots, to 6 figures, for the following integral 

 values of n: o-io, 15, 20, 30, 40, 50, 75, 100, 200, 300, 400, 500, 750, 1000. 



Jahnke and Emde, Table XXII, first 9 roots, 3 decimal places, integral 

 values of n 0-9. 



Roots of: 



(log 2 - y)J n (x) + ~ Y n (x) = o. Denoted Y n (x) = o in table. 



Airey: Proc. London Phys. Soc. 23, p. 219, 1910-11. First 40 roots for 

 n = o, i, 2, 5 decimal places. 



Jahnke and Emde, Table X, first 4 roots for n = o, i. E decimal places. 

 Roots of: 



Denoted N (x) and NI(X) in tables. 

 Yi(x) = o. 



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

 Roots of: 

 JQ(X) (log 2 - y)J (x) + - Y Q (x) = o. Denoted /(*) Y (x) = o. 



Ji(x) + (log 2 - y)Ji(x) + -'Fi(j) = o. Denoted Ji(x) + YI(X) = o. 



Jo(x) - 2 (log 2 - y)J (x) + - Y (x) = o. Denoted J (x) - 2Y (x) = o. 



2 



(log 2 y)Jo(x) -\ Y Q (x) = o. Denoted ioJ (x) YQ(X) = o. 



2 



