i 136 ) 



If again we substitute V y — 1 == z then the different terms assume 

 the following form : 

 yHy r K3 



r* y k dy C VZ 



= 2| /3 ll +*» +*<*=!> 3 - + W-W- '^l + 



I 3 2/ 5 ■ 3/ 7 ~ 



So we find for i? a series of the following form : 



E-- 



tc' b, 2c s 3 



j/3 (3/ + 5/ Pa + l! Pl ' 

 the coefficients p having the following values : 



Pl — 2^/3.2 



2 2 . 6 



J' 4 '/ dy . 



— r c =- the factor I 7 // — 1 is always positive between 



l 

 the limits 1 and 4. So the value of the integral lies between the 



J 4 dy T 4 dy 



rp - and y"k\ 7/=y where y represents the mini- 



i i 



mum value and y" the maximum value of y between the given limits. 

 Here we have y' = 1 and y" = 4t. The value of the term of order h 

 of the series for E lies therefore between the terms of order k of 

 the two series : 



and 



n c' 2c 4 3c 6 



E' — ~ 2t\— A 1 



3! 5! 7! 



E>=-2t\ i ^ + 2 ' {2cy ' 3 ' (2c)e 



3! ■ ' 3! 7! \ 



and as the ratio between two consecutive terms of these series 



verges for terms of high degree to zero, the series for E will also 

 converge. 



