ON CALCULATION OF MATHEMATICAL TABLES. 



253 



Zeros of Ber, Bei, and other Functions. 



In series of descending powers of x, Ber x contains the factor cos 8, where 

 x 1 1 25 



8= 



8x\ 2 Ifa? 384s* \ 2 



+ 



If 8=-^-.*, 



H 



2 -Z 1 + 1 W2 + i+-i 2 +- 25 - 

 2 87 8x 16* 2 384.T' 1 



If a:=(l+"+X4-— +-j + , then by Lagrange's Theorem, 



x x* ar x 



*=0 + £ + l+^. + izM + 



(3 p p» p« 



If (3 = I — - — + e) TC ^2, the zeros of Ber x are given by 



P» = P + 1 a + ,Vi + ^ 



19 3 v 2 



3899 



8(3 16p a 384(3* 128(3 4 15360(3° 

 For the zeros of Bei x, (3= ( n + - J tc v'2 



For Ker x, (3 = (?^=- 1 - *) TC V 2 



and for Kei x, (3= In—- )tc\2. 



The zeros of the functions Ber'a;, Bei'x-, etc., are given by 



= _3 _S\/2_ 39 27\_2_ 621 



P " Y 8y 16y 2 128y ! 128y< 5120y 5 



