22 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



1.83 Newton's Interpolation Formula. 





(x - a) (x - a - ti) ..... (x - a - n - iti) ^ n ,/ x 



(x-a) (x-a-h) ...... (x - a - nti) , 



n+i\ 



where has a value intermediate between the greatest and least of a, (a + nti), 

 and x. 



1.831 



/(a + **) - /(a) + i A/ (a) + ^ Ay (a) + ^-')- a ) A'/ (a) 



o * 



+ ...... + wA^-yo) + Ay (a). 



1.832 Symbolicall) 



2. f(a + nh) = (i + 



1.833 If w = /(a), MI = f(a + ti), uz= f(a + 2ti), . . . ., u x = f(a + xti), 



d 

 u x =(i + A) X u = e TXUQ. 



1.840 The operator inverse to the difference, A, is the sum, S. 



1.841 If AF(*) =/(*), 



where C is an arbitrary constant. 

 1.842 



