482 BELL SYSTEM TECHNICAL JOURNAL 



1 1 , ^ A. ■>(a ^■'^ ^ 



3!^* " 3! 2-4! ' V 2-'-5! 2-4! 





21.1' / 92.71 71.] 



>■)• / :) 



93.21 92.91 



'•^' 8^^- 4V^ ) + 



9' -2' / 2--3' 91-91 



l!g., = 1! - 62^=^+ 6-4 • - 



7 \ 7-9 7 



93.41 22-3' 



7-9-11 7-9 



2' -3! / 2- -4! 2' -3! 



2\q:, = 2\- e2-— +.M 4 



9 V 9-11 9 



2^-5! _42!Jd,+ _ 



9-11-13 9-11 



The way in which the succeeding terms of each series are to be 

 formed will be made clear by comparing the numbers just preced- 

 ing the fs in the p series with the numbers in the expansion of 

 1/(Vt' + 1 + ixt) into a power series in e. 



The series converge if e = ^u — 1 < 2. 



The q series are all represented by the single formula 



/ 2 \i+(^/2) ^/x , X ^ . X e 



1 + M/ \2' 2' " ' 2' 2 



2 \l+(x/2) 



1 +M 



1+ ^ /^^--2 



.V + 4 V 2 / 2 



xix + 2) / e\-(.v - 2)(.r - 4) 



+ 



{x + 4){x^b)\2j 2-4 



xix 4- 2) / e\=^ (.V - 2) (a- - 4)(.v - 6) 



(.r + ())(x + 8) V2/ 2-4-6 



x{x + 2) / 6 y (a- - 2)(.v - 4)(.v - 6)(.v - 8) 



■^ (A- + 8nA- + 10) V2/ 2 •4-6 -8 "^ 



I 



good for all values of e if a- is even ; good for e :^ 2 if a- is odd. Other 

 series are available for odd x and 2 < e but there is little likelihood of 

 their being needed. 



