Stolarsky mean

In mathematics, the Stolarskysche average or short the Stolarsky agent is a term introduced by Kenneth B. Stolarsky average, the generalized logarithmic means.

For two numbers and a parameter the Stolarsky agent is defined as

In this case, the limit is over all pairs to form with. In case of the limit value is the -th power of the derivative of the function and therefore actually true, as indicated, with the same.

Special cases

The Stolarsky agent has the following special cases:

Weighted Stolarsky funds

The Stolarsky funds can also be weighted:

Credentials

  • Horst Alzer: Optimal estimates for specific averages ( PDF; 141 kB)
  • Horst Alzer: inequalities for mean values. In: Archive of Mathematics Vol 47 ( 5), Nov. 1986 springerlink.com
  • Thomas Riedel, Prasanna K. Sahoo: A characterization of the Stolarsky mean. In: Aequationes Mathematicae 70, No. 1/2, Sept. 2005 springerlink.com.
  • Average
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