Ah. Thanks. So the most simplified version of your function is this:

You then defined, as mentioned above,

And your goal is to maximize correct?

Looking back at your post # 3, I think may have seen some of your problems. I think they might be in your syntax. When defining your functions, you have to use correct Mathematica syntax. Here's the generalized hypergeometric function in Mathematica:

Code:

HypergeometricPFQ[{1,1,1},{2,1+a},x-r x].

The extra braces, I would guess, are important.

In addition, I don't think Mathematica understands elided constraints of the form

.

Instead, list that as two separate constraints:

Unfortunately, I do not have a version of Mathematica that includes the NMaximize command, and I really don't see how to do this problem on WolframAlpha, because of the need to define several things before actually maximizing. However, I will give you the exact syntax that I believe should work, assuming this problem is doable in this manner:

Code:

f[j_,r_,x_,a_] := ((r x)^(n[[j]])Gamma[a + 1]Gamma[n[[j]]] Hypergeometric2F1[n[[j]],n[[j]], n[[j]] + a, x - r x])/(x n[[j]] Gamma[n[[j]] +
a](HypergeometricPFQ[{1, 1, 1}, {2, 1 + a},x] -
(1 - r)HypergeometricPFQ[{1, 1, 1}, {2, 1 + a}, x - r x]))
L[r_,x_,a_] := Sum[Log[f[j, r, x, a]], {j, 1, Length[n]}]
n = {1, 1, 2, 3, 4, 4, 150, 532}
NMaximize[{L(x,r,a),0<x,x<1,0<r,r<1,a>0},{x,r,a}]

Here the third line definition of n should be whatever your data actually is.

Try that and let me know how it goes.