Bessel- Clifford Function, and its applications. 515 

 Next, with Me^ipn (1), 



$ 2 2 + (0'-^=°' • • • .-,.<?> 



of the more general form of (5) in § 9 : a change is made 

 here in the dependent variable, putting 



'• 2 5+-vj+[?(« ? -i)-^+i)^gn«'=o ; . (2i) 



and taking q (q — 1) — i(i + 1 ), q = z .+ 1 or — i, 



'•^ + 2 ^ ( F + (a) !C = ' C M > 



w= Caj-j^), . . (23) 



so that we may write, symbolically, 



it} !±i / d \p it} l d \ 



rj = x n Ca»+i(jg), or ,2? » ( ^~ ) /°> or ^ n \T ) M ' ^^ 



2i-2 2i + ± 



p = , q — . 



A n n 



The pressure equation is 



Ip = -Mp 



Ir 



,2 



= -A^C 3 (#)C 3 {x)x » d 



i 

 -i 



= -AC^C,^-)^ rf«, .... (25) 



n n 



for which Lommel may be consulted in Math. Ann. xiv. 

 p. 510 ; but no simple general integral is obtainable, beyond 

 Laplace's case of n = 2. 



