﻿IG 
  Relation 
  of 
  Airij's 
  Integral 
  to 
  the 
  Bessel 
  Functions, 
  

   Table 
  I. 
  — 
  n 
  greater 
  than 
  z. 
  

  

  '■^\ 
  2-1123. 
  

  

  ^^Jn(^). 
  

  

  '' 
  /x2-1123. 
  

  

  Sr3 
  

  

  hn{z). 
  

  

  1 
  -2 
  

  

  •38666 
  

  

  2-2 
  

  

  •04007 
  

  

  •4 
  

  

  •32849 
  

  

  2-4 
  

  

  •02987 
  

  

  •6 
  

  

  •27459 
  

  

  2-6 
  

  

  •02203 
  

  

  •8 
  

  

  •24786 
  

  

  2-8 
  

  

  •01609 
  

  

  1-0 
  

  

  •18344 
  : 
  

  

  30 
  

  

  •01163 
  

  

  1-2 
  

  

  •14684 
  i 
  

  

  32 
  

  

  •00833 
  

  

  1-4 
  

  

  •11601 
  j 
  

  

  3-4 
  

  

  •00591 
  

  

  1-6 
  

  

  •09050 
  1 
  

  

  3-6 
  

  

  •00416 
  

  

  1-8 
  

  

  •06977 
  ! 
  

  

  38 
  

  

  •00290 
  

  

  20 
  

  

  •05317 
  

  

  4^0 
  

  

  •00200 
  

  

  

  Table 
  11.— 
  z 
  

  

  greater 
  than 
  n. 
  

  

  

  ^7x21123. 
  

  

  zhn{^). 
  

  

  ~-^X2-1123. 
  

  

  ^hn{.). 
  

  

  •0 
  

  

  •44549 
  

  

  2-2 
  

  

  •23779 
  

  

  •2 
  

  

  •50789 
  

  

  2-4 
  

  

  •07882 
  

  

  •4 
  

  

  •56606 
  

  

  2-6 
  

  

  •08616 
  

  

  •6 
  

  

  •61474 
  

  

  2^8 
  

  

  •24364 
  

  

  •8 
  

  

  •65228 
  

  

  30 
  

  

  •37869 
  

  

  1-0 
  

  

  •67264 
  

  

  3^2 
  

  

  •47653 
  

  

  1^2 
  

  

  •67093 
  

  

  3^4 
  

  

  •52457 
  

  

  1-4 
  

  

  •64282 
  

  

  36 
  

  

  •51447 
  

  

  1-6 
  

  

  •58528 
  

  

  3-8 
  

  

  •44412 
  

  

  1-8 
  

  

  •49714 
  

  

  40 
  

  

  •31901 
  

  

  2'0 
  

  

  •37982 
  

  

  i 
  

  

  — 
  

  

  Tables 
  for 
  shorter 
  intervals 
  may 
  be 
  constructed 
  by 
  inter- 
  

   polation. 
  The 
  first 
  table 
  exhibits 
  the 
  rapid 
  convergence 
  of 
  

   J„(^) 
  towards 
  zero 
  when 
  n 
  increases 
  beyond 
  z^ 
  even 
  when 
  z 
  is 
  

   very 
  great. 
  Q'his 
  convergence 
  soon 
  becomes 
  exponential. 
  A 
  

   formula 
  suitable 
  for 
  this 
  case 
  has 
  been 
  given 
  by 
  the 
  author"^. 
  

  

  The 
  limitations 
  to 
  be 
  applied 
  to 
  these 
  tables 
  are 
  well 
  

   defined. 
  When 
  z 
  and 
  n 
  are 
  exactly 
  equal, 
  the 
  error 
  in 
  the 
  value 
  

   of 
  ;in[z) 
  is 
  -0007 
  when 
  ^ 
  = 
  8, 
  and 
  -0006 
  when 
  z 
  = 
  20. 
  It 
  is, 
  

   in 
  fact, 
  fairly 
  constant 
  so 
  far 
  as 
  tables 
  have 
  hitherto 
  been 
  

   constructedf. 
  It 
  may 
  be 
  shown 
  to 
  affect 
  only 
  the 
  fifth 
  

   significant 
  figure 
  when 
  w= 
  100, 
  from 
  theoretical 
  considerations. 
  

   Other 
  portions 
  of 
  the 
  tables 
  have 
  a 
  mors 
  restricted 
  application. 
  

  

  * 
  Brit. 
  Assoc. 
  Report, 
  Dublin, 
  1908. 
  

  

  t 
  To 
  ?i 
  = 
  24. 
  Vide 
  Gray 
  & 
  Matthews' 
  Treatise. 
  

  

  