522 
[955 
955. 
THE NUMEKICAL VALUE OF Tli, = r(l+i). 
[From the Messenger of Mathematics, vol. xxm. (1894), pp. 36—38.] 
I DO not know whether the numerical value of Hx for an imaginary value of 
has ever been calculated; and I wish to calculate it for a simple case x = i. 
We have 
Hz 
= 1 + 
1 + |) 
l + g)*“* 
- Z\ *hl* 
1 + ;)‘ 
wherelhl denotes the hyperbolic logarithm. 
1 i 
+ I 
Hence, in particular, when z — i, we have 
1 + i . cos hi \ + i sin hi £. 
¿i 
1 + ^. cos hi §■ + i sin hi §. 
1 + ^ . cos hi f + i sin hi f. 
= \/(l + 1) . COS 0J + i sin 6 1 . COS 0! — i sin (j) 1 . 
V(1 + i) • C0S ^2 + i sin #2 ■ COS <f) 2 — i sin (f) 2 . 
a/(1 -f h) • cos $3 + i s i n $3 • cos 03 — sin 03-