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airy_ai

airy_ai(9.1);

Calculate

airy_ai-plot2d
plot2d(airy_ai(x),[x,-15,5]);

plot2d(airy_ai(x),[x,...

Calculate

airy_ai-exp-explicit-pi-plot2d-sin-sqrt
plot2d(airy_ai(x),[x,-15,5]);

plot2d(airy_ai(x),[x,...

f1(x):=1/(2*sqrt(%pi)...

f2(x):=1/(sqrt(%pi)*(...

Calculate

airy_ai-exp-pi-plot2d-sin-sqrt
plot2d([airy_ai(x),f1,f2],[x,-15,5],[y,-1,1]);

f1(x):=((exp(-((2*x^(...

f2(x):=((sin(((2*(-x)...

plot2d([airy_ai(x),f1...

Calculate

airy_ai-exp-pi-plot2d-sin-sqrt
plot2d([airy_ai(x),f1,f2],[x,-15,5],[y,-1,1]);

f1(x):=((exp(-((2*x^(...

f2(x):=((sin(((2*(-x)...

plot2d([airy_ai(x),f1...

Calculate

airy_ai-plot2d
plot2d (airy_ai(x), [x, -15, 5], [y, -15, 5]);

plot2d (airy_ai(x), [...

Calculate

airy_ai-pi-plot2d-sin-sqrt
plot2d ([C], [x, -15, 5], [y, -1, 1]);

A(x) := airy_ai(x) ;

B(x) := (1/(2*sqrt(%p...

C(x) := (1/(sqrt(%pi)...

Calculate

airy_ai

airy_ai(0);

Calculate

airy_ai

airy_ai(1000.1);

Calculate

airy_ai-pi-plot2d-sin-sqrt
plot2d ([A, B, C], [x, -15, 5], [y, -1, 1]);

A(x) := airy_ai(x) ;

B(x) := (1/(2*sqrt(%p...

C(x) := (1/(sqrt(%pi)...

Calculate

airy_ai

Run Example
(%i1)eq1:y=airy_ai(x);
(%o1)                           y = airy_ai(x)
(%i2) eq2:y=1/(2*(%pi)^0.5*x^0.25)*Exp(−2/3*x^1.5);
                                                 1.5
                                                x    2
                           0.28209479177388 Exp(------)
                                                  3
(%o2)                  y = ----------------------------
                                       0.25
                                      x
(%i3) assume(x<
5,x>
-15,y<
1,y>
-1);
(%o3)                  [x < 5, x > - 15, y < 1, y > - 1]
(%i4) linsolve([eq1,eq2],[x,y]);

rat: replaced -0.2820947917739 by -4821/17090 = -0.2820947922762
(%o4)                                 []
(%i5) 
Run Example
A(x) := airy_ai(x) ;
(%o1)                         A(x) := airy_ai(x)
(%i2) B(x) := (1/(2*sqrt(%pi)*x^(1/4)))*%e^((-2*x^(3/2))/3) ;
                                                       3/2
                                                (- 2) x
                                                ----------
                                    1               3
(%o2)                B(x) := ---------------- %e
                                          1/4
                             2 sqrt(%pi) x
(%i3) C(x) := (1/(sqrt(%pi)*(-x)^(1/4)))*sin(((2*(-x)^(3/2))/3)+(%pi/4)) ;
                                                     3/2
                               1              2 (- x)      %pi
(%o3)          C(x) := ------------------ sin(---------- + ---)
                                      1/4         3         4
                       sqrt(%pi) (- x)
(%i4) plot2d ([A], [x, -15, 5], [y, -1, 1]);
plotplot2d ([A], [x, -15, 5], [y, -1, 1]);
Run Example
airy_ai(inf);
(%o1)                            airy_ai(inf)
(%i2) 

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