Identric mean - Alchetron, The Free Social Encyclopedia

The identric mean of two positive real numbers x, y is defined as:

I ( x , y ) = 1 e ⋅ lim ( ξ , η ) → ( x , y ) ξ ξ η η ξ − η = lim ( ξ , η ) → ( x , y ) exp ⁡ ( ξ ⋅ ln ⁡ ξ − η ⋅ ln ⁡ η ξ − η − 1 ) = { x if x = y 1 e x x y y x − y else

It can be derived from the mean value theorem by considering the secant of the graph of the function x ↦ x ⋅ ln ⁡ x . It can be generalized to more variables according by the mean value theorem for divided differences. The identric mean is a special case of the Stolarsky mean.

References

Identric mean Wikipedia

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