TABLE 7. 

 SERIES. 



= x n + 2. jn-i y + ^-J *n-2 y + . . . 



(-!)... (n-m+i) ^ n _ w 

 w ! 



(i x) = i * 4- Mn ~ Ia> " rcfo-i) (M-2).y2 + _ _ + (d 





(-fcj! kl 

 3'~ 



(- 



ip 6^5 4- 



f(x+h) = f (x)+hf (x) + k ~ /"(*)+...+ ^ /<> (*) + rayl series. 



/ / \ / / \ , x f i \ , x2 * , - ^ n r , n \ Maclaurin's 



/ (x) =f(o)+ - )' (o) + - /" (o) + .../ () ( ) + . . . series> 



/ i\ i i i i 



= hm( i+-) w =i+ - - -f- - - + -- 4 -- . +... 

 V ;// i! 2! 3! 4 i T 



= i + x + -, H -- 1 H -- 1 -f- . . 



a x = l+x ] ga+ v - -^ + 



3! 

 .r i , i /x i \ " i /x i\ 3 



i **=~ + - 2 () + -i(v; + 



= O - - M* - O 2 + H* - O 3 - 



lg ( T + *) = X $ X 2 4- i A; 3 j .T 4 + . . . . 



== l f.ix .-ix\ X * * 5 * 7 



~ ~^i (t ~ 3! + ? ~ T"! 4 



cos .r = - (e'- r 4- g->) = i- H 1 +... = i_ versin .v 



7T T^ T "7 >v5 T *? C A"7 



. . i i i ' ^5 **' v5 *^ 



~ 2 " 6 2*4"5" + 2*4*6'7 



tan~ ! x = - cot. 1 # = a: # 3 H .r 5 - a- 7 4- ... 



7T I I I 



i , x 3 * 5 Jc 7 



smh s = ~(e*- e-*) = x + - + - + -,+... 



SMITHSONIAN TABLES. 



