38 FUNDAMENTAL POWER SERIES AND THEIR DIFFERENTIAL EQUATIONS. 
then 
glint) 
y = Af am4a x Rea CPE te 
[(m + 2) —(n)] [(n +2) -(-n)] 
and 
py = rAd amen ee mi j 
[(n + 2) —(n)] [(m + 2) -(-n)] 
when the elements are 
| Rise) Lamar! fA eae = 
1) = DP) 14S) == 
The series is BESSEL’S Series and dy =Ax’y is BESSEL’s Equation. 
y Y q 
In the particular case of the progression of elements p,, ... . bein 
Pp prog Pi P2 g 
oidiars Seoyselars P-3 P-9 P=; Po Pi Po Pes >. 
Be Ey 96 Ste Ole Ml ee Ee eee aed and A= -1 
(n-++2)2 op (+42 
ACh ms 28 ee os rs 
‘ ‘i (n+2)*—n4 ‘ {(m + 2)* — n*}4(m + 4)* — n4} i 
(46) 
(47) 
