EQUATION AND ITS TRANSFORMATIONS. 
825 
See art. 7. 
/ 
I l—x 
n + 2a* 
(n + 2)(n + 4) x s 
— &C.^6' 
' n + 1 2! 
1 (n + l)(n + 2) 3! 
n + 2 x 2 
(n + 2)(n + +) x % 
| St ft V.' 
' tH 1 2! 
1 (n+l)(n+2) 3! 
1 Gv 1 
(vii.) 1878. - “On the Solution of a Differential Equation allied to Djccati’s.” 
‘British Association Deport’ for 1878 (Dublin), pp. 469, 470. 
Proof that the coefficient of h i+1 in the expansion of e a ' /{x " +xh) satisfies the differential 
equation 
cl~u 
da? 
—a~u=- 
i(i+ 1 ) 
U. 
See arts. 8, 9. 
Writings referred to in § Y. 
(viii.) 1813. Poisson. “ Memoire sur les Integrales Definies.’ 
l’Ecole Poly technique,’ vol. ix. (cah. xvi.), pp. 236-239, 241. 
It is proved that if 
Journal de 
y= e 
0 
ba n 
— X n — • 
dx. 
dhy 
then y satisfies the differential equation -~- =n z ba n 2 y, and it is deduced from tins 
2 
result that the equation is integrable in a finite form when See arts. 20, 36. 
A relation between two definite integrals is also proved. See art. 26. 
(ix.) 1872. Glaisher. “ On the Evaluation in Series of Certain Definite Integrals.” 
‘ British Association Deport’ for 1872 (Brighton), Transactions of the Sections, pp. 
15-17. 
Investigation of the formula (8) of art. 21 by the process given in arts. 21, 22. 
Writings referred to in § YI. 
(x.) 1839. Gaskin. Senate House Problem. 
The solution of the equation 
clH 
dx~ 
+ 0 
a~u— 
iAv± i) 
u 
is given in the forms 
tt=cx-4fy cos(V,, H 
\dr) y/r 
MDCCCLXXXI. 
5 o 
