Roots of integral of Airy function (matlab)

Question

I want to solve the following equation

I am doing something wrong with the definition of the function but I still don\'t get it

function F=m         


        

Answer 1

Your integral seems to have no roots in [-15 -1] and converges to zero. I have tested it via plotting:

x0 = linspace(-20,20);
airyint = arrayfun(@(x0) integral(@(n) airy(n), x0, inf), x0);
plot(x0, airyint);

I also tested it via fzero() such as:

f = @(x) integral(@(n) airy(n), x, inf);
fzero(f, 0)

Output is as expected:

ans =

    115.8524

But it seems like every real numbers for x > 115.8524 will look like roots of this integral equation.

Additional:

fzero() is a function trying to find roots looking at the values of funtion between two dynamic intervals. If it catches minus and positive values, it is narrowing the interval to catch the root. But there is an error rate since you also can observe from this example. This equation will be zero only when x goes to infinity which means there is no real roots of this equation.