134 Mr. H. A. Webb and Dr. J. R. Airey on the 



VII. If a =^7, M(a, 7, #) can be expressed in terms of a 

 Bessel function. In fact 



M(i 7 , 7, *)=2 T_I • r(l+l) •/ • a" 5 *. 1^(4*) • (13) 



VIII. The Frr or Function = <f)(x) 

 2 



•J/" 



. dx 



2r 2 

 ^=.*-*.M(l,f,* s ) (U) 



The Incomplete y Function = y(n, x) 

 = \ e .t .dt 



%J0 



= ^.e- x .3D n .M(l,n+l,x). . . . (15) 

 Sonine's Polynomial = T (x) 



= i^L.M(-n,m + l,x). . • . (16) 

 ??i ! n! 



The Function of the Parabolic Cylinder 



1 7 ?l ,2 



= ( — 1) . e 4 . — (e ) 



= (if n is «v^n) 



(^.r^i) . e^ . M (- 1 1, i- 2 ), (17 «) 



and = (if n is oc?d) 



TC ~1 2 1 



(-j)^.r g) • «"* • «• • m (ip, I, w) • • (17 6> 



