Creating Airy Pattern WITHOUT bessel function and using Matlab's function for J1(rho) for values 0-10

I need to approximate the airy pattern without using the bessel function, but I cannot figure out how! I've been trying to come up with some way to do this for hours, but none of my code is working. I know that this can be done with the bessel function, and I've figured out how to code that:

X=[];Y=[];
x = -10:0.01:10;
I0 = 15; 
I = I0*(2*besselj(1,x)./(x)).^2;

plot(x,I)
ylim([-2 16])
grid on
title('Airy Pattern BUILT IN BESSEL f(x)')
ylabel('Normalized PSF Amplitude')
xlabel('Radial Coordinates')

r=0:10
J1=Jinc(r).^2
ai=((2*J1(r)/r) .^ 2)

But I need to do this exact same thing, except without the bessel function and for only the 11 values that are 0-10.

If anyone knows how to do this! That'd be great!

[John D'Errico]

So, the solution apparently needs a Bessel function. You don't want to use a Bessel function. We all want things in this world that are not realistic. You already have a solution to your problem, except that for some obscure reason, you have decided to ask for magic to happen.

You can expend the effort to write your own implementation of the necessary Bessel functions. But if your goal is to find someone else willing to do that implementation for you, sorry, but that is probably not going to happen, nor is it the purpose of Answers.

[Walter Roberson]

What is the purpose in avoiding the bessel functions? We could give the hypergeom definition of AiryAi or AiryBi, but would hypergeom be any more useful for your purpose than bessel would be?

[David Goodmanson]

Hello Candice, are you perhaps studying diffraction theory, with the idea being to confirm the (J1(x) / x)^2 expression by integrating a particular function over the surface of a circular aperture? That is certainly an eminently reasonable task.