$$B_y(x, z)= \frac{y^x}x2F1(x, 1 − z; 1 + x; y)$$
Note: 2F1 represents the Gauss hypergeometric function. I had trouble around its notation here.
I have this relationship between an incomplete beta function and a Gauss hypergeometric function. However, when I plot the two sides of the relationship for 0<y<1 and x>z>0, the graphs are not the same. Instead, they diverge. I then fixed y at y=0.5 and varied x and then z, but the graphs are still different. This then begs the question, when is this relationship true?
Urgent help will be highly appreciated. Thanks in advance.
The incomplete beta function definition that is expressed as a Gauss hypergeometric function:
$$B_y(x,z)=\int_0^yt^{x-1}(1-t)^{z-1}dt=\frac{y^x}x2F1(x,1-z;1+x;y)$$
The incomplete beta function as defined in MATLAB: $$I_y(x,z)=\frac{1}{B(x,z)}\int_0^yt^{x-1}(1-t)^{z-1}dt=\frac{B_y(x,z)}{B(x,z)}$$
What this means is that I was actually using $I_y(x,z)$ in place of $B_y(x,z)$ in MATLAB.