1204 

 Substitiitinnj this value in (9) we have 



00 j,2 00 



H„ {x) =: -, — <?^' ie ^ cos { xu ^ ) ^" \^~ '''■-'''" lin («) da 



00 00 5 



1 f , r2y.u u" / 7lJt\ 



— e^^ I e-~'^''H„ (a) da \e * cos\ xu \du. 







Changing « into — «, this giv^es 



5 



( IV' C ,. r — 2a«--«2 / n3l\ 



H„ (x) = -^— ^■"' I «"""' ^" (^') d(i ie "^ cosi xu \ dn {r) 



— 00 



and putting — u instead of a, the same equation leads to 





 1 r , r-2y.u--u- f n:t\ 



Bn {x) = e^' I e—'-'-^ H„ («) da I e * coslxu-{---\ dn 



00 00 



which, by the relation 



cos\ xu .— { — I)" cosl xu-\ 



is equivalent with 



^ 



h„ (x) = -^^e^' I e- ''' Hn («) da \e * cos f xu \ dn . (d) 



— GO 00 



Now, adding the equations (c) and ((/) we lind 



H„ (x) = ~-^ e^* I g- «■- H„ {(() .la \e 4 coslxu J du 



4 



where, putting u^v « 



5 



5 4 



te cos \ xu ] du ^ e \ e cost xv — — ax I dv^ 



CC 00 



1=^' /4 n:t\ r —4' 



= e cos I — ax -\ 1 I e cos xv dv . 



V5 ^ 2 j J 



According to formula {a) Art. 6, we obtain therefore 



\ e cos \ xu du = e cos \ — ax -A 



