290 M. A. F. Sundell on Galvanic Induction. 



where the arithmetical mean of the values of JL in a series is t 

 be used. 



The integral A is found by developing the function in a series. 



As - < 1, we have 



1 W 8 b 3.5 u 1 3.5.7 u 3 \ 



where 



t> 8.5.7... (2p + l) F B ; s =1 _ 



Hence 



A=42;:;(-i)^f + Wr^&. . («) 



By the theory of binomial integrals we have 



For the limits w=+landw= — 1 the first term in the right- 

 hand member is zero, and 



In the same manner we find 



J + l y_3f + l , 



If/? is an odd number 2g + l, the last integral of this kind is 

 wy/l — uHu\ and for p even = 2g the last integral is 



r+i 



I s/l—ifidu. It is easily found that the former integral is 



= ; thus all coefficients B p with an odd index disappear. The 



value of the latter integral is = — . If we ascend successively to 



the original integral, we find for p~2q:-~* 



P Wl^Afo- (2<?-l)(2?-3)(2 g -5)...3.1 . jr w 



Li V Udd -(2 q + 2) 2? (2 ? -2)...6.4 a-^- 3 > 

 if we denote by C 2? the fractional coefficient, which is =1 for 



1 



