﻿89G 
  Dr. 
  I. 
  J. 
  Schwa 
  tt 
  on 
  the 
  Summation 
  of 
  a 
  

  

  Then 
  since 
  

  

  h 
  

  

  X 
  ©J 
  = 
  0, 
  when 
  n^LO 
  (mod 
  h) 
  , 
  

  

  K 
  = 
  l 
  

  

  and 
  

  

  X 
  ®k 
  = 
  A, 
  when 
  n 
  = 
  (mod 
  A) 
  , 
  

  

  s 
  jfc_ 
  je=Aj 
  ir 
  X-, 
  = 
  7ig, 
  

  

  00 
  

  

  Adding 
  2/(«) 
  by 
  columns 
  we 
  obtain 
  

   »— 
  o 
  

  

  A®, 
  = 
  2 
  2^ 
  

  

  .«=i(® 
  cX 
  ) 
  6 
  L 
  e 
  ,5) 
  In 
  J 
  

  

  1 
  r 
  * 
  e 
  e 
  «-x 
  ^ii 
  1 
  v' 
  1 
  i 
  n 
  

  

  i 
  r 
  i 
  e 
  9 
  ^ 
  6-i 
  v 
  » 
  v 
  

  

  Now 
  

  

  2 
  ®;- 
  s 
  = 
  0, 
  when 
  w— 
  ft 
  or 
  b-n^O 
  (mod 
  A), 
  

  

  and 
  , 
  

  

  * 
  

  

  .n—o 
  

  

  X 
  @" 
  = 
  A, 
  when 
  n—1) 
  or 
  ft 
  — 
  n 
  — 
  (mod 
  A). 
  

  

  *c=l 
  

  

  We 
  must 
  therefore 
  consider 
  only 
  such 
  values 
  of 
  n 
  as 
  will 
  

   make 
  b— 
  n 
  = 
  £A. 
  

   We 
  then 
  have 
  

  

  for 
  n 
  = 
  0, 
  t 
  = 
  j 
  , 
  and 
  for 
  n 
  = 
  b 
  — 
  1, 
  £ 
  — 
  y. 
  

   Writing 
  ^ 
  for 
  the 
  integral 
  value 
  of 
  j 
  , 
  

  

  