2O MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



1.52 Table of Binomial Coefficients. 



fn\ ^^ 



G) G) (")' (,:) (,",) (,",) 



1.521 Glaisher, Mess, of Math. 47, p. 97, 1918, has given a complete table 

 of binomial coefficients, from n = 2 to n = 50, and k = o to k = n. 



1.61 Resolution into Partial Fractions. 



If F(x) and f(x) are two polynomials in x and f(x) is of higher degree than 



L_ ^pM i 1 



-i)l dcr- l l<t>(c) x-c\ 



where 



The first summation is to be extended for all the simple roots, a, of f(x) and the 

 second summation for all the multiple roots, c, of order p, oi-f(x). 



FINITE DIFFERENCES AND SUMS. 



1.811 Definitions. 



i. A/(*) =/(* + *)-/(*). 

 2. 



