28 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



1.879 Stirling's Formula. 



log (w!) = log \/27r + (n + -J log n - n 



, A 2 , (2* -4)! 



o<6<i. The coefficients AH are given in 1.86. 



1.88 



1. i + i! + 2-21 + 3 -3! + . . + ! = (+ i)! 



2. i -2-3 + 2-3-4+3 -4-5 + . ...+(+ i) (w +2) =-w(w + i) (w + 2) (w 



4 



3. 1-2-3 ....? + 2-3-4 . . . (r+ i) + ....... + n(n+ i) (n + 2) 



. . . . ( + r - i) 



_n(n + i) (n + 2) . . . . (n + r) 

 r+ i 



4. i-# + 2(^> + i) + $(p + 2) + ....... + ( + n - i) 



2- 2). , 



) (q-i) + (p-2) (q-2) + ....... (p - w) (q - n) 



- ( - i) (3^ + 39 - 2^ + i)]. 



6 ! \ b \ i 



o a(a + i) 0(0 + i) . . . . (a + n - i) 



_ b(b + i) . . . . (b + n) ___ a - i 

 (b + i a)a(a + i) . . . . (a + n i) 6 + i a 



