116 THE ROYAL SOCIETY OF CANADA 
The ne vast Of Jo Ji + à Ji Jo ++ Joe Ja +... 
“atest CE) 
D 2G)" 
se 2s+1 2s+1 tog SS ed ls+1! 
Co) 8G) Cr re ee 
ra ; og west? 
ence the general term simplifies to (—1)5 2 Re on = the 
general term of a . It follows that 
iS LIDIL — a ; therefore v = 2 
This proof associates, then, with the formula (38) the companion 
formula 
RS = tbh Sth it... (41) 
§ 16. This formula (41) leads fairly directly, as we shall show, to 
a formula described by Nielsen as ‘‘remarkable’’, namely 

SH F Q (2x sin ¢) sin ¢ dé (42) 
x 
(N. p. 65), where Q, (x) is the function = | sin (x sin ¢—vd) dd in- 
o 
troduced almost simultaneously by Lommel and H. F. Weber of 
Zurich (N. p. 48). For this purpose we start with the formula (N. p. 
67) 
ee 5 2s+1 
Qon ES = een (25 + 1D)° — — An? Jos+1 (x) ’ 
4 
MG = > “ss J'ESSAIE) 
which implies 
_ Now by (41) 
set = 2 (Jo J1++ Ji Je+ 24 Je Ts +...) 


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