PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. . ggj 



H 



+ -^;^~^ f^(lx-l){>n + fX-S) ...(m + n-r) /m + fx-r+ ... | 



= (-l)-" ^j=^ Im + a-r. { {m + n~V) ... (m + fx-r) 



Im ^ 



— ^— {m + fJ.—2) . . . (m + fl — r) + . . '. 

 + {-iy-^fJi(jl-l) ... (jx-r + 2) . r(m + fi-r) 

 + (-l)>Otx-l)...(M-. + l) } 



= (-If ^j=^ /fx-n { (fl-n) (/z_„ + l) ... (^_w + 7=T) 



= (-If ^.^ /^^. (_i/ ^ i_ . ^-»+'- 



jr — 1 / 1 \r — 1 



. X' 



-LJL^ ^ . <^ (-1) ^f.— »+r— 1— fi— 1 



I 



1 '^^ dx'-^ ■ a^-" 



r{r-\) d' d'-^ (-!/-' ^.^ + .-2-^ _ , 



1.2 d^ ■ ax'--' ^» "J 



= (-1)".^^- /jil=^(-l)'-:r— "^_( ^K^-— 1— ) 



= (-ir^=- /yu-nC-l/.r'-- 





= (_!)'' ^^ /jr:^ (_iy ^r_. nin-l)...(n-r+l) 



^»-^ 



= (-1)"-^:^ lll-n{-\) 



r A' + l 



/»« /w— r + 1 



.;^ a:"-'' /^t-w /w + lC-lX 



= ( — 1) — ^^ — -^ — sai{r—n)TT 



Im "T 



^+1 IfX — n /n + \ eUnnnr 



which coincides with (3). 



