PAPER BY MAX MAEGULES. 



311 



then we obtain the followiug equations for the determination of the 

 constants 





i-2+ A^ )a,-(^ -k 



/ = 5, 7, 9, . . . 



(11a) 



\ 



Apparently ai remains undetermined ; for the computation of the 

 others, following- the lead of Laplace, we write 



4:1c{i-\- 2) 



3A-(i + 2)+(i-2)t(t + 2)-(i-l)*(i+l)^ 



By the interchange of i with / + 2 a similar expression ir, formed for 

 -^— and then -i±- and in a similar manner for the subsequent terms of 



«,_2 (li 



the series, and by substituting these values in the above equation we 

 obtain a continued rapidly converging fraction. 



93 = 



95 = 



A'5=3A-. 11 + 7.9. 10, 

 Z5=4 k. G. 7. 8. 11, 



«3 



If in the second of equations (11a) we put a;,=q^ a^, then will -?also 



be determined, and the quotient has the same value as if it were com- 

 puted from the serial fraction 



- €(3 4 k. 7 



^'-a^-N^Z^ 



N,-Z, 



N,- . 



