Difference between revisions of "Mobius inversion formula"
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| − | Suppose that <math>f</math> and <math>g</math> are [[function|functions]] from the [[natural number|natural numbers]] to the [[real number|real numbers]] such that <math>f(n) = \sum_{d|n}g(d)</math>. Then we can express <math>g</math> in terms of <math>f</math> as <math>g(n) = \sum_{d|n} \mu(\frac{n}{d})f(d)</math> where <math>\mu</math> is the [[Mobius function]]. This formula is useful in [[number theory]]. | + | Suppose that <math>f</math> and <math>g</math> are [[function|functions]] from the [[natural number|natural numbers]] to the [[real number|real numbers]] such that <math>f(n) = \sum_{d|n}g(d)</math>. Then we can express <math>g</math> in terms of <math>f</math> as <math>g(n) = \sum_{d|n} \mu\left(\frac{n}{d}\right)f(d)</math> where <math>\mu</math> is the [[Mobius function]]. This formula is useful in [[number theory]]. |
{{stub}}[[Category:Number Theory]] | {{stub}}[[Category:Number Theory]] | ||
Revision as of 19:54, 13 March 2022
Suppose that 
and 
are functions from the natural numbers to the real numbers such that 
. Then we can express in terms of as 
where 
is the Mobius function. This formula is useful in number theory.
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