I just read a paper in which the authors used summation notation in several different ways. At first, I thought that my knowledge of the formula is inadequate. So, I reviewed the basics in here and here. Nonetheless, I'm still confused with the way they presented the formulas. The problem is that when I simulated the paper I found that some of the summations - as they used - are wrong and do not produce the desired results. I put some that notations here to be checked if they present same idea or there are some type of errors with them.
