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Beta and Airy Functions
06-27-2015, 11:19 AM
Post: #6
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;
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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



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