••(64) 



| a^e" 1 tf* = „m±Jp J z i eV.r (65) 



writing /i for (ux — jp + l)/p and integrating by parts, 



/«^»*B = 2 



f xe'-nfeW i dz 



>n tinned applies 



tion of which gives 



f zH-e*dz — zP4? 



J I - £ + £ (/ ^7 1} - , 



+ (-] 



y/x( / ,-l)...( / x-r + l) 



which, if (m - p + l)/p be substituted for //, takes the form 



... + (— l) r (wt-p+l)..«(w»^-rf+D , ete< I _ (68) 



The definite integral ///dtf between the limits and oo 

 will often be required. When the index of the exponential 

 factor is negative, the integration maybe effected as follows: 



If, as above, we put p =(m-p + l)/p, then (m + l)/p = 

 H + 1, and if also we put u == im* so that 



dx/clu = l/(pup ny 1 ) (69) 



we have the result in the form of the second Eulerian 

 integral, viz.:— 



vhieh gives also, by ma 



11. Special cases of integr 



