I remember from my student years that we could generalize mean and standard deviation in one formula. The formula defines a statistical characteristic over a positive natural number, called degree, far as I remember. When the degree is zero, you would get the mean (denoted $\mu{}_0$), when the degree is one, you would get the standard deviation (denoted $\mu{}_1$).
Unfortunately, I cannot find such a thing online. Is there such a number? What would that formula be.