 
 
 
7.3.19  Airy functions
The Airy functions of the first and second kind are defined by
| Ai(x)= |  |  | ∫ |  | cos | ⎛ ⎝
 | t3/3+x t | ⎞ ⎠
 | dt,  
Bi(x)= |  |  | ∫ |  | ⎛ ⎝
 | e− t3/3+sin | ⎛ ⎝
 | t3/3+x t | ⎞ ⎠
 | ⎞ ⎠
 | dt. | 
Let f and g be two entire series solutions of
 w″−x w=0 .
Then
| Ai(x)=Ai(0) f(x)+ Ai′ (0) g(x),  
Bi(x)= | √ |  | (Ai(0) f(x) −Ai′ (0) g(x)), | 
where 
f(x)=∑k=0∞3k(Γ(k+1/3)/Γ(1/3)) x3k/(3k)! and g(x)=∑k=0∞3k(Γ(k+2/3)/Γ(2/3))
x3k+1/(3k+1)!.
The Airy_Ai and
Airy_Bi commands
compute the Airy functions.
- 
Airy_Ai and Airy_Bi take one argument:
x, a real number.
- Airy_Ai(x) and Airy_Bi(x) return the values of
the Airy functions.
Examples
 
 
