( ^41 ) 



\ah'-\-{2ac\-'ób')T'-]-{c'^\-2üe^(](nl)r']--ó\.rr' \ L^/cT^lAr- i r/r<)4-/>•VM^- 



^- H 



5 



48 



because = 



^_ , = 1 -f T- + t' + . ., ill u hirl, (1—//) X 



1 is sub- 



tracted ill llic second iiiember. Su we get liiially : 

 /43 44 



= t' + (1 — /.) T^ + (l_/>_Jj t\ 



From this follows a<2,aiii 

 11 



a- = 1 — « — oa-/> 4 3A' + 2ac =1 — /> I - a" — 2 1 aV> + 22a'?>' — 5/*' + 

 5 7 



44 



4 a'c — lOrt/^c 4- c' — Da\/ + 6^^^ -^ 2ae = 1 — h — <]. 



5 



So it follows also from the logarithmic equation (2) alone that 



^=1, 



while the two others pass according!}- into 



6 



■ 41, 4- 3/,^ + 2c = 



5 r 



36 44 ('^) 



_ 20/; + 22// — 5/.=' 4 c — 1 Obc 4^ r - id 4- 6/;r/ 4-- 2^' = 



Now the two lirsl e(iuations of («) and (|i) yield immediately 



1 _ 13 



~ ~ 50 * 



h =: 





Substitution of these values in the two last equations of(«)and(ji) 

 yields : 



16 



.- d + 2r 



391 

 250^ 



== 0; 



from which 



64 

 d :=: ; e 



875 



14 4953 



d + '2e -] = 0, 



5 ^ ^ 17500 



1359 

 35000 



So in this way we find every time two coefficients at the same 

 time. It is self-e\'idcut that if we only want to determine a and b, 

 the expansions need not be carried further than t', which simplilies 

 the above considerable Hut we wished to determine also tiie coefli- 



