Is this what you are asking for?
In[1]:= normpoints = Table[{\[Gamma], Norm[N[AppellF1[1/2, 3.5, 0.5, 5, 8.8/(8.8 - \[Gamma]), 4.4/(
4.4 - 5.3 \[Gamma])]]]}, {\[Gamma], 0, 15}]
Out[1]= {{0, 3.65714}, {1, 1.80643}, {2, 2.2696}, {3, 2.06301}, {4, 1.7368}, {5, 1.38028},
{6, 1.03249}, {7, 0.712053}, {8, 0.411022}, {9, 0.183567}, {10, 0.413092}, {11, 0.521346},
{12, 0.591746}, {13, 0.642558}, {14, 0.68141}, {15, 0.712268}}
In[2]:= ListPlot[normpoints, Joined -> True]
