Definition:Hölder Mean/Negative Exponent with Zero Parameter

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Definition

Let $x_1, x_2, \ldots, x_n \in \R_{\ge 0}$ be positive real numbers.

Let $p$ be an extended real number.


Let $\map {M_p} {x_1, x_2, \ldots, x_n}$ denote the Hölder mean with exponent $p$ of $x_1, x_2, \ldots, x_n$.


For $p < 0$ and at least one $a_k = 0$, the Hölder mean is defined as:

$\ds \map {M_p} {x_1, x_2, \ldots, x_n} = 0$


Also see

  • Results about the Hölder mean can be found here.


Source of Name

This entry was named for Otto Ludwig Hölder.


Sources