In this paper, a general Mõbius transform on is discussed, and a pair of dual Mõbius inversion formulae are given, based on which some properties of the Mõbius transforms involving the k-th order divisor function and central binomial coefficients are obtained. A directly simplified proof of a known result, as a special case of our theorem, is also given.
Ping XI, Yuan YI.
On Generalized Mõbius Inversion Formulae. Acta Mathematica Sinica, Chinese Series, 2009, 52(6): 1135-1140 https://doi.org/10.12386/A2009sxxb0141
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