98 A-rt. 4.— M. Kuniyeda : 



'where p h any reid constant, <z > and q, a are certain constants, 

 then the hehaiùour of the coefficient a„, ax n^x>, is determined 

 asymptoticallij as f(jU()ir.< : 



(i) If q = \, <'■ — -, or tJie .sinyulfwiti/ is of the type 





then 



(9) a„r^ —a-iP^ie-^SiiP^^sml^akii-ity-î)-} 



(ii) If <:q <\, a = (\ +q)'^, or the singularity is of the type 



then 



(10) "n^V^-]^,:7]^}"'('^*)''^'"'' ''' exp |^[^-y,i+'^-(i^j-^J-]iJ, 



(iii) //' < g <; 1, ^/ = (;^ — g}-^^ ^y^. ^/,g ninyalarity is of tJic type 



f(y\ — 1 .^"(sin è'm + '■ COS ir77r)/(l-z)'^ / ^ > . = , < ; \ 



z*^-^ - {\-zY U > 0, < g < 1 ; ' 



then 



A" heiiuj the xarne as in the case {ii). 



Ill Case in ivhich the Singularity is of the Type 



_J: //(I- -f^ /lo^ 1 V 



57- ^\ ^' now pass to llie case in wliieli f{z) luis a singularity 

 of the type 



^^ ^ (1-^f \ ^^ 1-J ' 



