﻿Type 
  of 
  a 
  Family 
  of 
  Trigonometric 
  Series. 
  897 
  

  

  A 
  similar 
  form 
  is 
  obtained 
  for 
  

  

  x> 
  ,, 
  n 
  

  

  6, 
  = 
  2 
  p 
  > 
  

  

  n 
  =o 
  b 
  + 
  nh 
  1 
  

   and 
  we 
  Lave 
  

  

  6-^. 
  

  

  Now, 
  let 
  r 
  lh 
  = 
  y, 
  then 
  

  

  d 
  1/ 
  rf\ 
  

  

  ar 
  /i 
  \ 
  ay/ 
  

  

  and 
  

  

  Replacing 
  p 
  { 
  and 
  p 
  2 
  in 
  (7) 
  by 
  their 
  values 
  from 
  (3), 
  in 
  

   terms 
  of 
  y, 
  (I) 
  becomes 
  

  

  B 
  = 
  l(").-V^ 
  v 
  |Q(4)"[# 
  7 
  {i^ 
  

  

  t(6-K&) 
  -tN 
  _i(b-Kh) 
  

  

  (8) 
  

  

  wherein 
  P 
  y 
  stands 
  for 
  the 
  expression 
  within 
  the 
  square 
  

   brackets 
  in 
  (8). 
  

  

  Carrying 
  out 
  the 
  indicated 
  differentiation 
  and 
  separating 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  20. 
  Xo. 
  155. 
  Nov. 
  1913. 
  3 
  P 
  

  

  