 
 
 
5.9.19  Airy functions : Airy_Ai and Airy_Bi
Airy_Ai and Airy_Bi take as arguments a real x.
Airy_Ai and Airy_Bi are two independent solutions
of the equation
They are defined by :
| | Airy_Ai(x) | = | | (1/π) | ∫ |  | cos(t3/3 + x*t) dt | 
 |  | Airy_Bi(x) | = | | (1/π) | ∫ |  | (e− t3/3 + sin( t3/3 +
x*t)) dt | 
 | 
 | 
Properties :
| | Airy_Ai(x) | = | Airy_Ai(0)*f(x)+
Airy_Ai′(0)*g(x) |  | Airy_Bi(x) | = | | √ |  | (Airy_Ai(0)*f(x)
−Airy_Ai′(0)*g(x) ) | 
 | 
 | 
where f and g are two entire series solutions of 
more precisely :
| | f(x) | = | |  | 3k | ⎛ ⎜
 ⎜
 ⎜
 ⎜
 ⎜
 ⎝
 |  | ⎞ ⎟
 ⎟
 ⎟
 ⎟
 ⎟
 ⎠
 |  | 
 |  | g(x) | = | |  | 3k | ⎛ ⎜
 ⎜
 ⎜
 ⎜
 ⎜
 ⎝
 |  | ⎞ ⎟
 ⎟
 ⎟
 ⎟
 ⎟
 ⎠
 |  |  | 
 | 
 | 
Input :
Airy_Ai(1)
Output :
0.135292416313
Input :
Airy_Bi(1)
Output :
1.20742359495
Input :
Airy_Ai(0)
Output :
0.355028053888
Input :
Airy_Bi(0)
Output :
0.614926627446
 
 
