86 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



The first seven roots are: 



Xi = O, 



Xz = 0.8l6o7T, 



x 3 = 1.928571-, 

 x 4 = 2.93597T, 



3.806 



The roots are: 



3.807 



The roots are: 



3.808 



The roots are: 



* 6 = 4-97287T, 



#7 = 5-97747T. 



cos x cosh x = i. 



(Lamb, 1. c.) 



3.809 The smallest root of 



xi = 4.7300408, 



X2= 7.8532046, 

 #3 = 10.9956078, 

 #4 = 14.1371655, 



x b = 17.2787596, 

 x n = \( + I)TT 



(Rayleigh, Theory of Sound, I, p. 278.) 



cos x cosh x = i. 



xi = 1.875104, 

 x 2 = 4.694098, 



*3= 7^54757, 



X* = 10.995541, 

 x$ = 14.137168, 



*6 = 17-278759, 



x n = \(2n I)TT n>6. 



i (i + x 2 ) cos x = o. 



xi = 1.102506, 



X2 = 4.754761, 

 * 8 = 7.837964, 



x^ = 11.003766, 

 X 5 = 14.132185, 

 x& = 17.282097. 



(Schlomilch: Ubungsbuch, I, p. 354.) 



- cot B = o, 



is 



(1. c. p. 355.) 



