Beta and Airy Functions
06-27-2015, 11:19 AM
Post: #6
 roadrunner Senior Member Posts: 425 Joined: Jun 2015
RE: Beta and Airy Functions
(06-24-2015 06:48 PM)parisse Wrote:  http://people.math.sfu.ca/~cbm/aands/page_446.htm

That method becomes unstable outside a range for z of about -10 to 10. I believe that is because the calculator is trying to divide one huge number by another huge number to get a small number.

How can one calculate the airy function outside that range?

Code:
 local f(z) begin  local t,t2,k,p,p2;  t:=1;  p2:=1;  for k from 1 to 80 do   p:=3*k;   p2:=p2*(3*k-2);   t:=t+p2*z^(p)/(p)!;   if t == t2 then return t; end;   t2:=t;  end;  return t; end; local g(z) begin  local t,t2,k,p,p2;  t:=z;  t2:=0;  p2:=1;  for k from 1 to 80 do   p:=3*k+1;   p2:=p2*(3*k-1);   t:=t+p2*z^(p)/(p)!;   if t == t2 then return t; end;   t2:=t;  end;  return t; end; export ai(z) begin  0.355028053887817*f(z)-  0.258819403792807*g(z); end; export bi(z) begin  (0.355028053887817*f(z)+  0.258819403792807*g(z))*√3; end;
 « Next Oldest | Next Newest »

 Messages In This Thread Beta and Airy Functions - douganc - 06-24-2015, 11:20 AM RE: Beta and Airy Functions - Tim Wessman - 06-24-2015, 02:39 PM RE: Beta and Airy Functions - Gerald H - 06-24-2015, 03:27 PM RE: Beta and Airy Functions - DrD - 06-24-2015, 03:33 PM RE: Beta and Airy Functions - parisse - 06-24-2015, 06:48 PM RE: Beta and Airy Functions - roadrunner - 06-27-2015 11:19 AM RE: Beta and Airy Functions - Gerald H - 06-27-2015, 12:15 PM RE: Beta and Airy Functions - parisse - 06-27-2015, 12:41 PM RE: Beta and Airy Functions - roadrunner - 06-28-2015, 12:47 AM RE: Beta and Airy Functions - Gerald H - 06-27-2015, 05:25 PM RE: Beta and Airy Functions - douganc - 07-20-2015, 08:10 PM RE: Beta and Airy Functions - roadrunner - 07-20-2015, 08:55 PM

User(s) browsing this thread: 1 Guest(s)