PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. ^ 581 



+ ^-y-^^ fJL(iJL—l)(m + fX-S) ... {m + jJL-r) /m + ix-r + ... j 



= (-1)'' ^^ im + ix-T. f (m + /x-l)... (M + /x-r) 



_ii!L(m + /x-2) ... (m + fx-r) + . . .' 



+ (-l)'-X/;t-l)...0u-/- + 2) .r(w + /X-y) 



+ (-i)Xft-i)...(/i-/+i) } 



= (-If ^^^ //T^ { (/X-«) (^-W + 1) ... (yU-W + T^) 

 /m > 



r 



w + r 



= (-^^ is^ '''-'' *^"'^ 57- -^^-"^ 



r d u, d^^ ( — 1)*"" |<i— »+r— 1 — !«,— 1 



~i~d^ 'ax"—^ ' ^-^ 



. r(r-l) d' ^. d'-'' (-l/~' ^^^,^ + ._2-,I=:2 _ I 



1.2 c?^ ■ dx'-'' tT-^ ' ' 



n — ft, ( 



Im \ 



= (-ir.^- /^,i3^(_i)'-.— _^(..-^) 



a; '* , , ^.^ ^ n d ■ X 



= (-IT -V- //i^ (-ir ^'""-7^ 



/m dx 



= (-ir i^ /^ (-ir ..-. "C-D^-c— ^1) 



/m a: 



= (-ir^=- //x-«(-ir 



//w /«—/• + ! 



, ^.u. x'^'^ /fx-n /n + l(-iy . , , 

 = {—Vf -^- ^ 1— .sm (/• — ») TT 



= / ^Ni^+l /M-^/^ + 1 sin>^7^ 

 which coincides with (3). 



