828 
MR. J. W. L. GLAISHER OX RICCATTS EQUATIOX. 
(xx.) 1872. 
“On a Differential Equation allied to PtiCCATi’s." ‘Quarterly 
Journal of Mathematics,’ vol. xii., pp. 129-137. 
r 00 cos ctfc 
The equation is (1), and the definite integral | . 2 applied as in art. 29 
to obtain the general integral in the form 
o o 
u—x l+1 
1 ciy ye”* + cjr ax 
x dx 
and also in Boole’s form (29) : the results are transformed so as to give the symbolic 
solution of Riccati’s equation, which is integrated also by Boole’s method. See 
arts. 29, 30, 33, 34, 35, 38. 
(xxi.) 1876. - “Sur une Propriety de la Fonction e Vir .” 
respondance Mathematique,’ vol. ii., pp. 240-243, 349-350. 
Proof of the theorem 
9_2b+1/ !L 
dx 
x 
>n+\ 
d \« +1 , , 
—) e 4x —eJ x 
dx 
by means of the integral 
See art. 36. 
b_ 
e -a.T 1 - x ? ( jx = 
MdP -3V(aS) 
Wa 
‘ Nouvelle Cor- 
(xxii.) 1876. - “ On Certain Identical Differential Equations.” ‘Proceedings 
of the London Mathematical Society,’ vol. viii., pp. 47-51. 
Generalisations of the theorem in (xxi.), as for example 
fj \ n r 1 ] ?—1 / rl \«+l 1 
\ 71+~ I I Us \ I / - 
dx 
X 
\dx 
and other similar results. See arts. 33, 36. 
(xxiii.) 1879.-“ On a Symbolic Theorem involving Repeated Differentiations.” 
‘Proceedings of the Cambridge Philosophical Society,’ vol. iii., pp. 269-271. 
The theorem is (50) of art. 40, viz. 
pax 
—=( —)«2 \n\ 
X v 
1 d _\» 
x dx x 
and the proof is the same as in art. 41. 
