-04 Mr Bobb, Discusmm of a diference equation relating to 



Consider now the oxpiossiou 



cosh ft) — 1 



eosh DUO — cosh (o ' 



We may expand luuuerator and deuoiniuator in po\Yevs of ro 

 and the series ai"e always convergent. 



Thns 



cosh (0 — 1 

 cosh mm — cosh to 



0)^ CO* ft)* 



- — I 1 h + . . . 





4! ^ U! 



Thns — .- " T has the limit ^ ^ for w = and for 



cosh into — cosli co //r — 1 



(0 > it has always a smaller value. 



Let 7 now be kept constant in our series and let (?/, (fa', Os\ ••• 

 be the limiting values of the coethcieuts as (o approaches zeiu 



We have 



(,; = (jj = 1, 



It is thus clear that the coethcients a^, a^, a^, ... are respec- 

 tively less than tu\ a/, a/ .... 



Now let 



V = \^1- 2x 



1 ., 1.3 , 1.3.5 , 



the series being convergent when 



We shall write this 



f = 1 - ?), .r - 6., a- - bs A^ - 64 a"» - . . . . 



