A range of proposed aether-dragging theories could explain the null result but these were more complex, and tended to use arbitrary-looking coefficients and physical assumptions.
Other finalists will be assigned to by means of a draw, using coefficients as a basis.
Superior shapes for the frequency response can be obtained using coefficients derived from a more sophisticated design procedure.
Intuitively, this finds the filter that is as close as you can get to the desired response given that you can use only coefficients.
The procedure to go back and forth between these bases is to use Clebsch-Gordan coefficients.
Added terms are simplified using coefficients.
Use the as coefficients to form a polynomial .
It is speculated that a number system like this would use coefficients such as in the expression , that are not actually real numbers.
Since only the relative weights are relevant, any weighted mean can be expressed using coefficients that sum to one.
Several more complex formulae have been proposed which use different coefficients for different rep numbers and sometimes even for different exercises.
