mean well power

A generalized mean, also known as power mean or Hölder mean, is an abstraction of the Pythagorean means including arithmetic, geometric and harmonic means.

Definition

If t is a non-zero real number, we can define the generalized mean with exponent t of the positive real numbers a1,. ,an as

Properties

The case t = 1 yields the arithmetic mean and the case t = −1 yields the harmonic mean. The case t = 2 yields the root mean square. As t approaches 0, the limit of M(t) is the geometric mean of the given numbers, and so it makes sense to define M(0) to be the geometric mean. Mean well power supply. Furthermore, as t approaches ∞, M(t) approaches the maximum of the given numbers, and as t approaches −∞, M(t) approaches the minimum of the given numbers.

The generalized mean is a homogeneous function of its arguments a1,. , an. That is, if b is a positive real number, then the generalized mean with exponent t of the numbers ba1,. , ban is equal to b times the generalized mean of the numbers a1,. CORP MAXIM INTEGRATED PRODUCTS MCMASTER-CARR SUPPLY CO MEAN WELL MEMCOR-TRUOHM INC MEPCO METERMAN FROM FLUKE (FORMERLY MEAN WELL. , an.

Generalized Mean Inequality

In general, if −∞ ≤ s < t ≤ ∞, then M(s) ≤ M(t) and the two means are equal if and only if a1 = a2 =. = an. That follows from the fact that for −∞ ≤ t ≤ ∞, that can be proved using Jensen's inequality.