Zero Frequency Basis Equation for Discrete Sine Transform So, I'm evaluating the Discrete Sine transform Basis functions and I found on the internet the following picture:



So, I may be getting the point wrong, but, if the 2D DCT equation is: 



Then the Discrete Sine transform shall be:


Then, it is clear that for the lower frequency (u=0,v=0) all cosines will be 1, but in the case of the sines all will be 0 (for frequency=0), therefore, the basis function for the lower frequency, in the sine case, will be zero, right?

Is the upper left image (u=0,v=0) correct? It should be constant, right? (btw: It shall also be zero, right?)
I think I got it: 

While in the DCT there are definitions of the DCT that make cos(0) when u and v are zero, this does not apply to DST (see: https://en.wikipedia.org/wiki/Discrete_sine_transform). 

In the DST definition, there is always a +1 or a +1/2 adding to the frequency. 

This explains why it is not zero and also the graph above. It varies 
(for u=0 and v=0) because the content of the sine is not zero.