1879.] 



the Values of the Theta and Zeta Functions. 



357 



§ 6. It is convenient also for the sake of completeness to place here 

 the values of the functions for u—0, K, ^K', &c. 



u. 



Qu. 











mm 











K 



2*K*" 









iK! 







* 



00 



K + ^K' 



q 



7T 







2K 



mm 



IT* 











2iK! 



,mm 

 ~2 1 — i— 







K 



K + 2^K / 

 2K + 2*'K' 







, 2*K* 

 2 — T- 



\®um 

 -r 1 —. — 



7T 4 



. ,2*Jc'm 



^ i~ 







00 

 Mr 



~K 



*V 



§ 7. It follows from the values of 0^ and Hm in § 3 that if 



7T 



A=?S*(l + &) i , 



* The value of Z(2iK') is by mistake given as on page 164 of the "Fundamenta 

 Nova." 



