03/16/2011, 12:18 AM

perhaps x {y} z is the mean ONLY for 0 < y < 1

and x {y} z for y > 1 is simply the (y-floor(y)) th iteration of x {floor(y)} z.

but that has troubles : the definition is piecewise and the iterations are not uniquely defined for fractional iterations.

and x {y} z is not analytic.

and x {y} z for y > 1 is simply the (y-floor(y)) th iteration of x {floor(y)} z.

but that has troubles : the definition is piecewise and the iterations are not uniquely defined for fractional iterations.

and x {y} z is not analytic.