Beta and Airy Functions

[roadrunner]

(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;