408 THEOREMS RELATING TO A GENERALIZATION OF BESSEL’S FUNCTION. 
{Sm}? 2p{ Tn f+ art {Jab - 2... -{ =, Ter) 
(De aemse oy Ot 
foe eee eee 
r ae 2r 
7 25) Gears aa ape) 
4 Qr—r) , 2 ae or). \ 
f pA ty pl) CPM ae] (| 
(Cf. Trans. R.S.E., p. 110 (26).) 
ST oy(%)T oY) — 2PIy()Tin(y) + 2p (@)Jin(y) -— - > - 
begl(cee Unmet yt Sajak _(w@+pyy , @+pyy(e+ Py? _ a 
= { 1 Tp? ae a err De af {1 Tee + [2}°(4/? ihe i (73) 
1 2 2 2 | las 
Jp) tm + Jpn) [141 = zUa(a oat) | [2] [4 aren ol enen es a oe ; : . (74). 
E,(iz)E,( targa ay Fe—aln tA = Salts pete 
pL he — 2 Te  Miaalinsen (18) 
and a similar form for 2". (Cf. Proc. Lond. Math. Soc., series 2, vol. iii.) 
1 yr” . 
me) pF RA | 2 Vea ee ae 
2(1+p*) .. +p") - (tp)... +p") ora 7A 
2 [27 +1]! } (76) 
< a [40+ 2] Pane 
aa 
(Cf. Proc. Edin. Math. Soc., Theorem of LomMst, vol. xxii.) 
It is plain that great numbers of such theorems may be found and expressed in 
various forms by means of the transformations belonging to H,(«)-, but the examples” 
given above will suffice to illustrate the notation. 
