Transform of Möbius

the transforms of Möbius should not be confused with the Transformation of Möbius.

---- The transformed of Möbius of the function F definite on the strictly positive entireties, is the function Tf definite as follows:

$(Tf)\; (N)\; =\; \backslash \; sum\_\; \{D\; \backslash \; mid\; N\}\; F\; (d)\; \backslash \; driven\; (n/d)=\; \backslash \; sum\_\; \{D\; \backslash \; mid\; N\}\; F\; (n/d)\; \backslash \; driven\; (d)$,

where μ is the Fonction of Möbius.

(The notation D | N means that D divides N .)

This function is thus named in homage to August Ferdinand Möbius.

The reverse transformation T^-1f is given by

$(T^\; \{-\; 1\}\; F)\; (N)\; =\; \backslash \; sum\_\; \{D\; \backslash \; mid\; N\}\; F\; (d)$

See too

• Formula of inversion of Möbius

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